It always takes me twice* with numbers. Yesterday, I puzzled as to how the time path of climated costs simulated in the Stern Review could lead to annual costs of 5% and 20%. Richard Tol politely pointed out in the comments that this is an annuity. My mistake was to discount the costs at .01 instead of .01%. This is a common mistake made by dolts and idiots.
Anyway, discounting at .01% is about the same as not discounting at all. If you add up the red line costs in Figure 6.5d of the Stern Review (see my link above, or scroll down to yesterday's post) and average these over the 200 years of the analysis, the average cost is about 5%.
I still see two problems here:
- The high end cost scenario in Figure 6.5d leads to an average annual cost of about 5%, the low end of the annual cost range offered by the Stern Review. Where does the additional costs, "up to 20%", come from?
- The language of the Stern Review is still incorrect. The 5% loss of GDP that might result from climate change "now and forever" doesn't happen now, and doesn't last forever, ... unless we can annuitize those costs of climate change, and we can't. We (i.e., the living) can enjoy low costs for a long period of time and then, about 2100, the living must suffer as all heck breaks loose.
The "now and forever" language must be considered an intentional distortion designed to get everyone's attention, and it has. The problem is, these now and forever costs aren't correct.
Not discounting at all can be ethically correct but not economically correct. With our savings and investment decisions we all reveal that we take the future less seriously than the present. In order to balance sometimes competing social goals, equity and efficiency, it is always a good idea for an economist to present benefits and costs discounted at different rates. The Stern Review presents one rate as far as I can tell so I'll fill in the gaps. Based upon my reconstruction of the high cost scenario in Figure 6.5d (this one includes all costs excluding the higher weighting of low-income countries), the net present value of the net benefits of mitigation (benefits - costs) is:
- 4.43% of GDP (undiscounted)
- 4.37% of GDP (discounted at .01%)
- 1.03% of GDP (discounted at 1%)
- 0.25% of GDP (discounted at 2%)
The conclusions of the Stern Review must be clarified. We have simply got to do something about climate change if we think a $1 loss of GDP in 2200 is the same as a $1 loss of GDP right now. If we discount the future, at the real rate of long term borrowing (2%), this conclusion is not so clear.
Ethically, we can say that the appropriate discount rate is zero. Economically, we can't, and that's why the interpretations of this analysis presented to the media, and then repeated by the media is so troubling.
Update: I just left this in response to a question in the comments section of yesterday's post:
My enthusiasm for climate change mitigation is dampened as the benefits approach the costs. Both estimates are point estimates and have large error bands around them. There is a good chance that the costs will actually outweigh the benefits, due to statistical uncertainty, even when the net benefits are positive.
But yes, I think we should be doing something. I'm an advocate of a higher gas tax, carbon trading and public research into alternative fuels. But, I think we should start slow and ramp up over time as the costs of climate change become more clear.
Another update: More than twice with numbers (see Tol's comment below).