Recent empirical research has shown that output and GDP per capita in the aftermath of natural disasters are not necessarily lower than before the event. In many cases, both are not significantly affected and, surprisingly, sometimes they are found to respond positively to natural disasters. Here, we propose a novel economic theory that explains these observations. Specifically, we show that GDP is driven above its pre-shock level when natural disasters destroy predominantly durable consumption goods (cars, furniture, etc.). Disasters destroying mainly productive capital, in contrast, are predicted to reduce GDP. Insignificant responses of GDP can be expected when disasters destroy both, durable goods and productive capital. We extend the model by a residential housing sector and show that disasters may also have an insignificant impact on GDP when they destroy residential houses and durable goods. We show that disasters, irrespective of whether their impact on GDP is positive, negative, or insignificant, entail considerable losses of aggregate welfare.