Climate Tipping and Economic Growth: Precautionary Saving and the Social Cost of Carbon

The optimal reaction to a pending productivity shock of which the expected arrival time increases with global warming is to accumulate more precautionary capital to smooth consumption and to levy a carbon tax, proportional to the marginal hazard of a catastrophe, to curb the risk of climate change. The carbon tax holds down the stock of greenhouse gases, so that the risk of catastrophe decreases and less precautionary saving is needed. We also allow for conventional marginal climate damages and decompose the optimal carbon tax in two catastrophe components and a conventional Pigouvian component. Further, the productivity catastrophe is compared with recoverable catastrophes and with a catastrophe shock to the temperature response. Finally, the trade-off between adaptation capital and capital used for production is analyzed.