Brad DeLong carries on the discussion about discounting and the Stern Review, responding to a critique by Partha Dasgupta that has already been the subject of heated discussion. As Brad says, all Dasgupta’s assumptions are reasonable, and his formal analysis is correct
But … The problem I see lies in a perfect storm of interactions:
This brings me to one of my favorite subjects: the equity premium puzzle and its implications, in this case for the Stern Review. I’ll try and explain in some detail over the page, but for those who prefer it, I’ll self-apply the DD condenser and report
Shorter JQ: It’s OK to use the real bond rate for discounting while maintaining high sensitivity to risk and inequality.
Stern, and nearly everyone else in the debate so far uses a model based on expected utility theory. There are very strong reasons to go this way. First, expected utility has the property of dynamic consistency, which means that, if you make a plan, anticipating all possible contingencies, you’ll want to continue with that plan over time, whichever contingency arises. No other choice model has this property except under special conditions.
Second, expected utility theory allows a single utility function that simultaneously determines attitudes to intertemporal wealth transfers, interpersonal redistribution and risk reduction (transfers of income between states of nature). With the plausible technical assumption of constant relative risk aversion, (almost) everything is determined by a single parameter (called eta in the Stern report), which measures the substitution of elasticity of income.
The big problem is that observed market outcomes aren’t consistent with EU theory. This problem is partly because people don’t act in accordance with EU (as shown in experimental studies) and partly because markets don’t work in the smooth and frictionless way assumed in standard finance-theory models.
The most important problem in this respect is the ‘equity premium puzzle’, and the closely-related ‘risk-free rate puzzle’. The equity premium puzzle is that for plausible choices of eta, the real bond rate should be somewhat higher than it it has been on average (it’s close to the ‘correct’ rate at present), and the rate of return to equity much lower.
Historically, real returns to investors from the purchases of U.S. government bonds have been estimated at one percent per year, while real returns from stock (“equity”) in U.S. companies have been estimated at seven percent per year, a difference of six percentage points. By contrast, for reasonable choices of eta, the difference should be no more than half a percentage point. The equity premium puzzle can be resolved by assuming very high values of eta since risk aversion increases the premium. But high values of eta imply a high discount rate, so the risk-free rate puzzle is made worse.
There’s no generally agreed way of resolving the equity premium puzzle, but, as I’ve suggested above, the explanation should reflect some combination of individual preferences and market failure. If you accept that you get a couple of policy conclusions.
(i) When discounting riskless cash flows, the real bond rate is appropriate for governments and private individuals
(ii) When valuing risky cash flows received by individuals, the (large) market premium for risk should be applied
(iii) (Less general agreement on this one) When valuing risky cash flows received by governments, the (small) premium derived from expected utility theory should be used.
(iv) Any attempt to apply EU reasoning consistently across domains of time, risk and income distribution will lead, as Brad says, to a perfect storm of contradictions.
With this in mind, we can look again at some contributions to the debate.
Stern uses a low discount rate but wants to use a high risk premium when considering uncertainty and income distribution. In my view, this is reasonable.
Nordhaus wants a high discount rate on riskless income to match market data, but this data concerns risky cash flows.
Dasgupta shows that applying Stern’s eta in a world with an unlimited supply investment opportunities yielding 4 per cent produces implausible outcomes. The 4 per cent rate sounds reasonable because expected returns to capital are generally higher than this. But the riskless market bond rate is only 1 or 2 per cent. If an unlimited supply of riskless 4 per cent investments actually existed, an unlimited arbitrage would be possible. This is another way of looking at the perfect storm problem.
DeLong wants sensitivity analysis for higher values of eta. Again, reasonable, but I think the case for a value near one is quite strong.
John Quiggin 
No doubt fortuitous, but Stern’s departure from the UK Treasury this week was announced just the day after Gordon Brown’s budget preview in effect rejected his recommendations to apply one per cent of GDP to tackling emissions (Brown reckons adding the price of a couple of beers to air tickets will suffice to do that job and that GDP next year will be up by 2-3%, not down by 20% as claimed by Stern’s “now and forever” derived from his 0.1% social discount rate.
As I said here, the risk premium depends on the covariance between unexpected returns and unexpected variations in utility (typicially, the business cycle), not the variance of the return. AFAIK, there’s little reason to think that unexpected returns to reducing global warming will be correlated to the business cycle, so the risk premium for discounting the returns to reducing greenhouse gas emissions is probably close to zero.
For the low-probability catastrophic cases, losses from climate change will dominate the business cycle effects, so a risk premium is appropriate.
I was just jumping on to say what Stephen Gordon already said. Two issues – one the measurement of the equity risk premium – there was a lot of investigation a couple of years ago that suggested that the 6% number which is generally quoted around town is actually much higher than reality – there is a lot of success bias in there (i.e. the data doesn’t consider companies dropping out of the stock market) and there is also a lot of generally poor data in there – see the book Triumph of the Optimists for more on this point.
Second, standard CAPM theory (which is where equity risk premia come from) suggest that there is no return for diversifiable risk. To give a non global warming example, if you invest in an insurance company which has huge exposure to catastrophes, you should expect a return which is the same as, or lower than, the long bond rate, because you are getting a diversifiable risk which should improve your overall portfolio.
To me, that seems madness – you should get more money for taking a risk – but the result would tend to support the idea of using the real bond rate to assess global warming costs and benefits. There is some real-world support for the theory, by the way – if you look at the returns and variance of listed general insurers in Australia, you will find that they have a higher variance and lower return than the banks, suggesting that shareholders are happy to provide capital at high risk provided that risk is uncorrelated with the wider equity markets.
John, the fact that there’s uncertainty doesn’t mean that there’s a risk premium.
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