Discounting, Declining Utility, Disasters
& Climate Change Decisions.
“The best laid plans of mice and men gang aft agley.”
Nobody says that `The ill-laid plans of careless idiots often lead to glory’, though reading biographies of successful business men and politicians suggests it does sometimes occur. In looking at the future, mankind has shown for millennia in song and story an asymmetric perception of the likelihood of different unforeseen outcomes. We accept that “If it can go wrong, it will” is a poetic exaggeration, but “If it can go right, it will” is contrary to all common experience. The balancing proposition is rather “If it can go right, it just might.”
Because we judge that uncertainty increases with distance in time into the future (and quite often in a chaotic world increases sharply with time – meteorologists will explain), we extend our perception that the unforeseen is more likely to be malign than beneficent into regarding a bet on a future outcome as more risky the longer dated is the outcome. This is, the Unit judges, the root of our habit of discounting the future. Ingrained from past generations is the idea that at any moment in the future we may well find that our plans are going astray, but that serendipitous success is far less probable.
We not only discount the future, we distrust it. That distrust is a principal reason for accumulating wealth; as a reserve against the unexpected. The quite commonly observed behaviour of populations who discount the future industriously saving when they are well aware that they can expect negative real returns on their savings is a manifestation of this distrust of the future. It is simply that at that point the distrust outweighs the time discount. Looking to climate change one consequence to be expected, when and if the generality of economic agents accept that it introduces further uncertainty into the future, is some increase in savings rates.
We can expect mankind’s collective decision making to discount the future on the basis of our long standing appreciation that in our game against nature, the unexpected cards that slip out of nature’s sleeve will arrive at random moments, more of them will show red than black in our accounts, and they will accumulate through time. That rate of discount will rise somewhat if perceived uncertainty increases.
Many observed rates of time discount are, in this view of things, compounds of rate of discount and distrust of the future. They are conceptually difficult to apply to future investment decisions because while time discount is central to evaluating investment options, levels of distrust of the future are central to the different issue of how much to spend on insurance of one form or another. The two types of decision are only conceptually relatable if the marginal dis-utility of a future loss is firmly linked to the marginal utility of a future gain. The two marginal functions need not be equivalent or equal, but they must bear a defined relation to one another. It would be a great mental convenience to economists if such a long-term defined relation was found, but the Unit has not yet discovered a statistical demonstration of a link. Nor has the Unit encountered economic agents whose individual insurance and investment decisions support such a relation in practice.(1)
One part of observed time preference rates can, of course be taken out of consideration when looking at climate change. In part, we discount future benefits to ourselves and to individuals that we know because we expect individuals to die. The uncertainty here is the date of death, not its occurrence. The horizon for climate change is uncertain, but may be taken to be a date when all individuals now present (Solon perhaps excepted) have passed on (2). The potential beneficiaries of any action we take are our social and genetic heirs, a group which benefits from the law of large numbers and consequent lesser uncertainty. Our time preference rates for such benefits are therefore much lower than those which influence investment for more immediate benefits.
From the above arguments, the Unit’s view is that the time discount rate which should drive a model of decision for investment to minimise damage from climate change is low, but probably somewhat less low than previously “observed“ social time preference rates. Nonetheless, important as the discount rate must be, the discounted expected benefits do not have a cardinal value for decision making because the conceptually different distrust and insurance motivation is also present.
Poverty is largely relative.
Marginal utility of income is usually looked at in a context of static analysis. In those terms, it declines unequivocally, and the rates of decline are relatively well identified. For climate change, we have to consider whether that finding holds under dynamic analysis. Observation suggests that the social marginal utility of income over time in growing economies declines much less than in the static case.
The major point here is that poverty and the sense of being less than rich have been found to be largely relative. Study after study has demonstrated and deepened this perception. It seems probable, a priori, that most people in society are less eager for an extra 1% of income than they were 50 years ago, but it is evident that the utility of that extra 1% has fallen much less than one would have expected from an application of the static rate of decline of marginal utility. And concern for poverty is a social phenomenon; we are discussing here a dynamic social marginal utility of income which is not well estimated, but is clearly greater than the static rates that have been estimated hereto.
There is a further conceptual point. In the static case, the underlying utility functions of the individuals are assumed unchanged. One of the changes that does occur with rising per capita average incomes is that the weights attached to benefits to others in people’s utility functions rises. (3) Concern for poverty, when in absolute terms there is so much less of it, is one example. There are a host of others. (4)
For our climate change decision model, the static estimate of declining marginal utility of income is not an available short cut. It might be possible to estimate a declining social marginal utility of income in growing economies, but to apply that requires strong assumptions about the appropriate underlying utility function or functions.
“100 dead in traffic accidents this week” is a filler. “100 dead in plane crash” is a front page lead. (newspaper truism)
It was quite irking (5) that for years the scientific discussion of climate change ignored the seemingly obvious point that adding heat to a complex, chaotic heat-driven system of water and air flows was almost certain to quickly produce a greater incidence of extreme weather conditions. Headlines, flooded houses and rising insurance premiums finally brought the point home, but economists’ analysis of climate change is still catching up.
How fast the incidence of floods and extreme temperatures (plus droughts and some of the other plagues of Egypt) can be expected to rise is still poorly estimated. All that can really be said from such modelling as the Unit has encountered is that is that we can expect the rise to continue on an exponential steeper than that for the less unstable elements of climate change. The Unit’s working assumption is therefore that this element will be a rising proportion of the damages due to climate change
Transport economists were the first to note that as a society we are willing to spend much more per likely life saved from disasters averted than from everyday routine accidents averted. Much observed spending on flood defences fits the same picture. That is to say, if we apply the same decision rules to averting damage from climate change, we will value damage to people due to the “disaster” element of increased extreme weather incidence very much more highly than damage due to the slower acting “routine” elements of change. (6)
From work in transport economics, a rough range of the values of this multiplier of the value of a life lost in a disaster over routine fatalities is from 4 to 100. The Unit proposes to work with 4 for climate change. This choice is arbitrary (7); but The Unit feels that the very high (daft?) values will not stand up to the pressure of decisions needed in face of a rising stream of expected “disasters”. Intelligent survey and experiment should produce a better founded figure in due course.
In principle, the value of life to which this multiplier is applied should rise with rising incomes. It is not only that people increase the value they put upon their own lives as they become richer; they also increase the value they put upon the lives of others. And the proportional increase in the value that they put on the lives of others can be expected to be greater than the proportional increase they apply to the value of their own lives.
“Denn ja.”
When the Emperor Franz Josef started the First World War with this phrase, the analysis of outcomes and risks offered by his officials was outstandingly faulty. But he did his part, deciding on the available evidence and his judgement. The decision-makers on climate change (and unless mankind manages to wipe itself out, there will be a stream of them running for generations) will decide in the same way. What can we do to provide better analysis than did those be-medalled Austro-Hungarians?
What we cannot do and cannot expect to do is to provide a cardinal list of the measures that it is worth taking to minimise the risks (8) of climate change. Using approximate discount rates, we can now sort measures into approximate ordinal merit order, but that merit order needs testing against different plausible valuations of the benefits to be obtained. Independently, we can help arrive at another merit order concerned with measures to “insure” against outcomes to which society appears likely to be particularly averse. But the balance between the two merit orders and how far down them we should go at a given date are judgements that the social decision-makers must take.
We and our successors can and will refine those merit orders to a degree even beyond the imaginations of the most intrepid Unit members. Further, we can and should set in hand a body of systematic analysis of what future generations are likely to value. If we look back a century or three and imagine what our ancestors would have chosen for us if they had made such very long-dated decisions (9), most modern observers are likely to feel uncomfortable at that prospect. If we are to place major investment bets to benefit future generations, it is only sensible to do what we can to make it likely that the eventual “benefits” will not be too unwelcome.
Should you wish to comment, an email to solon@usesolon.org may draw a response.
.3. A clear pair of macro examples are the rising concerns in Britain and in the USA through the 19th. century for the welfare of the subjects of empire and of the red Indians. Nothing similar occurred in previous empires.
4. E.g., if Krakatoa exploded now, it would be seen as a world wide disaster. When it happened, it was reported as an interesting natural phenomenon.
.5. Irking to such people as, e.g., the climate disaster study team at Munich Re.
6. This argument evades important dynamics. When a once in 50 years flood becomes a 4 yearly event, does it become routine?
7. The former French Government that was badly damaged electorally by the wave of some thousands of excess deaths in the hot summer of 2003 might prefer a higher value.
