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Abstract We perform two tests that estimate the mass of the upper tail of the distribution of aggregate US tropical cyclone damages. Both tests reject the hypothesis that the distribution of damages is thin tailed at the 95% confidence level, even after correcting for inflation and growth in population and per capita income. Our point estimates of the shape parameter of the damage distribution indicate that the distribution has finite mean, but infinite variance. In the second part of the paper, we develop a microfoundations model of insurance and storm size that generates a fat tail in aggregate tropical cyclone damages. The distribution of the number of properties within a random geographical area that lies in the path of a tropical cyclone is shown to drive fat tailed storm damages, and we confirm that the distribution of coastal city population is fat tailed in the US. We show empirically and theoretically that other random variation, such as the distribution of storm strength and the distribution of damages across individual properties, does not generate a fat tail. We consider policy options such as climate change abatement, policies which encourage adaptation, reducing subsidies for coastal development, and disaster relief policies, which distort insurance markets. Such policies can reduce the thickness of the tail, but do not affect the shape parameter or the existence of the fat tail. [ABSTRACT FROM AUTHOR]