Using an endogenous growth model with physical and human capital accumulation, this paper considers the sustainability of economic growth when the use of a polluting input (e.g., fossil fuels) intensifies the risk of capital destruction through natural disasters. We find that growth is sustainable only if the tax rate on the polluting input increases over time. The long-term rate of economic growth follows an inverted V-shaped curve relative to the growth rate of the environmental tax, and it is maximized by the least aggressive tax policy of those that asymptotically eliminate the use of polluting inputs. Unavailability of insurance can accelerate or decelerate the growth-maximizing speed of the tax increase depending on the relative significance of the risk premium and precautionary savings effects. Welfare is maximized under a milder environmental tax policy, especially when the pollutants accumulate gradually. (C) 2012 Elsevier B.V. All rights reserved.