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| Devangshu Datta: The compounding paradox |
| Devangshu Datta / New Delhi Jul 17, 2010, 00:41 IST |
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In 1626, Peter Minuit, the Dutch Governor of the New Netherlands, bought Manhattan off a tribe for $24-equivalent — about half a cent per acre ($0.005). By 2000, assessed land value on the island core of New York was $830,000 per acre.
Did Minuit get a bargain? No. By the compounding formula (a principal of half a cent grows to $830,000 over 374 years), the appreciation is 5.2 per cent per annum. Any Delhi land-shark would sneer at a property market where values doubled every 14 years.
This is long-term compounding where a small sum invested at moderate return (ex-inflation) yields a huge amount compounded over a long time. It directly impacts economic policy. Examine Anthropogenic Global Warming (AGW) and the suggested policy in that light.
The sums in play are large. So are the time-frames. IPCC’s climate science models have very large variations in estimated impact. If AGW continues unchecked, between 3 per cent (minimum hypothesis) and 90 per cent of global GDP (maximum) will be affected by 2100.
Nicholas Stern wrote the influential Economics of Climate Change in 2006. He said it was probable that 20 per cent of 2100 GDP would be affected if AGW was not tackled now. He calculated that 1 per cent of 2006 GDP would have to be committed to mitigate AGW. In 2008, he reviewed his estimates and said 2 per cent of current GDP was required for anti-AGW activity.
Global GDP has grown at a trend rate of over 3 per cent since 1990. That is when Brazil and India restructured and the Soviet bloc abandoned communism. The long-term trend is closer to 1-2 per cent. Reversion to a lower trend is likely as BRIC-land becomes more prosperous and growth moderates in those parts.
If AGW effects were mitigated, compounding over 2006-2100, global GDP in 2100 would range between 2.7 times 2006 GDP (at 1 per cent growth), six times (at 2 per cent) or 16 times (at 3 per cent).
Stern suggests recurrent spending, of course, to stave off AGW.
Assume the 2010 anti-AGW expenditure “protects” 2100 GDP and 2011 anti-AGW spend protects 2101 GDP and so on. Calculating an internal rate of return (IRR) on that “protection money” shows IRR must be somewhere between 3 per cent and 6 per cent (depending on trend global growth). In every case, the protection money’s IRR would have to be at least twice, or thrice, the assumed trend rate.
This is possible, in theory. China, India, Japan and the US itself have demonstrated that much larger chunks of global GDP can grow for long periods at multiples of the global trend rate. But the specific policy actions advocated for anti-AGW equate to scaling down energy consumption to avoid spewing CO2. That doesn’t promise anywhere near the IRR an investor would want. This is one major reason why there is so much resistance to current anti-AGW policy.
Anti-AGW advocates fudge by talking of the “social discount” rate. The real IRR of anti-AGW spending is low (in fact, it’s near-zero). But since it helps protect vast future wealth, the positive externality is high. According to this logic, all our descendants capture that positive externality. But this is cold comfort for an investor.
Larry Karp of UC Berkeley, proposes an alternative concept of hyperbolic discounting (HD). HD draws on behavioural science. People care more about returns in the near future and less about distant returns. So, HD applies falling long-term rates of return. That’s elegant. But convincing investors about its efficacy may be difficult since fixed rates with higher returns are available.
Perhaps there is another way. If you accept Stern’s conclusions and climate science consensus, formulate anti-AGW policy that offers much higher real IRR. Would major incentives for R&D in green energy do the trick? One way or another, anti-AGW policy must resolve the compounding paradox.
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