There is broad consensus among economists that unmitigated climate change will ultimately have adverse global economic consequences, that the costs of inaction will likely outweigh the cost of taking action, and that social planners should therefore put a price on carbon. However, there is considerable debate and uncertainty about the appropriate value of the social discount rate, that is the extent to which future damages should be discounted relative to mitigation costs incurred now. We briefly review the ethical issues surrounding the social discount rate and then report a simulation experiment that constrains the value of the discount rate by considering 4 sources of uncertainty and ambiguity: Scientific uncertainty about the extent of future warming, social uncertainty about future population and future economic development, political uncertainty about future mitigation trajectories, and ethical ambiguity about how much the welfare of future generations should be valued today. We compute a certainty-equivalent declining discount rate that accommodates all those sources of uncertainty and ambiguity. The forward (instantaneous) discount rate converges to a value near 0% by century's end and the spot (horizon) discount rate drops below 2% by 2100 and drops below previous estimates by 2070.