Inter-Generational Discount Rates

    1.                  A (an individual or group taking an economic      decision) usually incorporates in his utility function a positive  value  for benefits to B (any or all other parties affected).(1) However the greater the distance (which may be defined  genetically, geographically or socially) between A and B, the lower is A’s valuation of the benefits to B.

  2.                  Nonetheless, the greater the temporal distance between A and future Bs, the greater is A’s reluctance to discount benefits to these future Bs. That is to say, A’s long-term general discount rate declines with time.

  3.                  One root of this paradoxical observation may lie in the fact that A identifies particularly closely with his genetic or social heirs. Benefits to them are nearly equivalent to benefits to A personally. With the passage of time, the chance increases that any randomly chosen group of future Bs will include heirs of A. Moreover, the likelihood of action purely for the benefit of the heirs of A succeeding in its objective falls sharply with the passage of the generations. Therefore, at limit, the prudent action in the interest of the heirs of A is to regard all the future population as if they were heirs of A.

  4.                  To put this another way, A continues to apply his personal, risk-averse time discount rate to his heirs, but by degrees extends it to the whole of the future population. The further discount that he applies to benefits to contemporaries because they are not A’s falls away. The original social time preference rate which was a compound of individual A’s valuation of benefits to near contemporaries who were not A’s and A’s valuation of benefits to himself and those close to him slowly resolves into a process of approximation to the latter. In this view, a declining discount rate treats the next generation equitably. A does unto the next generation as he would wish to be done to.

  5.                  Since benefits from the survival and prosperity of B (other individuals, groups and species) figure in A’s underlying utility function, with rising wealth and accompanying reductions in direct threats to the well-being of A, benefits to B tend to acquire more weight in A’s marginal utility function. That is to say, A’s valuation of benefits to B will be reduced less on account of ‘distance’ as A’s wealth increases. Thus with greater wealth, A’s discount factor for time t+n starts from a higher valuation of current and future benefits to B, and from a closer approximation of A’s social discount rate to his personal time discount rate. That is to say, A’s social discount rate has less distance to fall to reach its long term values (2)

  6.                  As Solon sees it, this sketchy discussion takes us to somewhere near the probable date of the funerals of A’s putative children. It does not account for the anecdotal and (limited) experimental evidence that “observed” social discount rates over horizon’s of centuries and millennia may be much lower. As an explanation for that, Solon proposes a conjecture which he hopes that ingenious investigators will find ways of testing experimentally.

  7.                  Humans, Solon included, seem to find it difficult to quantify long periods of time (3). As a first approximation to the way in which we may conceive such periods, Solon conjectures that we tend to perceive years as getting progressively shorter the further we look into the past and the future. The form of this progression should, of course, be defined experimentally: Nevertheless, Solon would test first a logarithmic relationship if the Unit were to set about examining suitable data.

  8.                  The basis of this hunch of Solon’s is paradoxic. He thinks that he has noticed some such relationship in his own perception of the acceleration of the passage of time during his extended existence.

  9.                  Should Solon’s conjecture have substance, the first apparent conclusion would appear to be that time discounting does indeed become an increasingly inappropriate decision criterion the further the costs and benefits are located in the future. Unless, of course, the decisions fall into the metaphorical hands of computers with a consistent sense of time.

  10.              If by any chance a similar distortion of perspective applies to human perception of geographical, genetic and social distance, we may also have a clue as to why it is so hard to compare observed social and personal time discount rates.

   Should you wish to comment, an email to solon@use-solon.org may draw a response.

  1.  The value to the group, and in general to its members, of A’s possible views of the value of benefits to B are easily illustrated by three versions of a Russian story. B, Boris has a goat. A, Alexei, has not. Alexei encounters a forest spirit who grants him one wish. He wishes for Boris goat to die; benefits to Boris are negative in his utility function. Or Alexei does not care about Boris one way or another, so he wishes for a goat like Boris’s. Or Alexei is a shrewd villager, and wishes for a billy goat reckoning that he can mate it with the goats of Boris and the other peasants and do well out of his share of  the benefits in stud fees and  be happy at the idea of the increase in Boris’ and the other villagers’ well-being. The village of the third version is obviously more likely to survive and prosper. Russians who are not peasants tell the story in the first version, to explain the misery of peasant life.

 2.                This prediction appears, in principle, empirically testable.

          3. Stories of dinosaurs and humans co-existing are an illustration. And even scholars have some difficulty in bearing in mind that Cheops was further in Cleopatra’s past than she is in ours.