Comments on John Geanakoplos's "The Ideal Inflation-Indexed Bond and Irving Fisher's Impatience Theory of Interest with Overlapping Generations

American Journal of Economics and Sociology, The, Jan, 2005 by Robert J. Shiller

It is refreshing to hear an account of Irving Fisher's views on risk and indexation juxtaposed with an account of our modern concerns with the same issues. It is interesting for me to hear this, partly since it shows that many of the issues we worry about today were concerns 70 or more years ago, and thus perhaps that these issues are indeed as deep and fundamental as we now think they are. But I found this history-of-thought presentation most interesting because it clarifies, by starting with simple notions that were on Irving Fisher's mind and moving forward, some of the critical issues concerning the innovations of indexation and Social Security reform.

John's paper with Martin Shubik (1990), described here, is really a deep theory of indexation, a theory that I think Irving Fisher wanted to have but could not get with the theoretical apparatus of his day. As evidence that Fisher wanted this, I show a few quotes from his 1911 book, The Purchasing Power of Money.

Irving Fisher appreciated that index number theory is a central issue for economists because it will be applied to the specification of intertemporal contracts:

   Perhaps the most important purpose of index numbers is to serve as
   a basis of loan contracts. (1911: 208)

I would put this as saying that since index numbers have their most important application in long-term contracts, index number theory ought to be considered a topic in theoretical finance.

Fisher also appreciated that indexation of contracts is not something that should be thought of as an issue of "fairness" or "justice," even though much of the debate about it today tends to be put in these terms. Discussions of the importance of indexed bonds speak of the unfairness of a situation in which the real value of a debt has been eroded by inflation. Discussions today of Social Security reform and the indexation of benefits also often center on doing the fair or just policy toward Social Security beneficiaries. But instead, the issue should be how indexed contracts as part of a portfolio strategy, or social risk-sharing strategy, can be used to promote a broader purpose of real risk management for all parties. Fisher wrote:

   In the first place, it should be pointed out that though there is
   a gain or loss [on loan contracts due to unexpected price changes]
   there is not necessarily any "injustice" wrought because of a
   change in the level of prices. ... Each party knew or should have
   known that the price level might change, and took the risk.
   (1911: 209)

Fisher, in his many researches on index numbers, was struggling with the central difficulty of defining an indexed contract that will be useful at large for contracts when there are many goods:

   Suppose, for example, that a lender receives back purchasing power
   over an amount of goods of the kinds he wished to use, equivalent
   to that he lent plus interest. Suppose also that, during the period
   of the loan, these goods appreciate relatively to others. Then the
   lender really gains, since he can now get more of other goods in
   exchange for those it was his original purpose to use.... To the
   borrower, however, the appreciation of the goods the basis of which
   repayment is made, relatively to the goods he is engaged in
   producing, might be regarded as causing him a loss. The same
   purchasing power over the goods, on the basis of which he is to
   make repayment, means in such a case, a greater purchasing power
   over the good he is engaged in producing.

   It is clear that no one kind of goods is a fair standard. An index
   number intended to serve as a standard for deferred payments must
   have a broad basis. (1922: 212-213)

   In this connection it may be well to call attention to another
   standard of purchasing power of money which has sometimes been
   suggested for adjusting contracts. This is the utility standard.
   According to this, each person would be expected to receive or
   pay back marginal utility equivalent to what he had lent or
   borrowed. But the marginal utility of the same goods is different
   for different persons at different periods of life. Hence, no such
   standard can be objectively applied. (1911: 220)

Fisher here shows clear awareness that defining optimal index numbers for use in intertemporal loan contracts is difficult, since people can have reasons for differing preferences about what goes into the index. He has an intuitive notion that somehow using a broad index is best overall but cannot articulate just what is the theory connecting the notion with a concrete index number formula.

John's paper with Martin Shubik (1990) has what I most admire: a theory that is both original and actionable. The theory is original in that it provides a rigorous justification of indexation in terms of that stellar economic concept, Pareto optimality. It is actionable in that it suggests how the price index for use in indexation could be defined. It shows a sense in which something like Fisher's "utility standard," or in more modern terms, a "superlative index," is indeed the right answer.