2023 FUTURE OBSERVATORY

5328 SPECIAL HYPOTHESIS OF INFLATIONARY EXPECTATIONS

 

Let us take the example of one individual who is asked to contract for the supply of a repeat purchase good at some time in the future. This example is chosen since it offers a more realistic example of price-setting than market-clearing by some form of auction (to an informed public) which is the starting point for much of neo-classical economics. Here, there is no direct balance of supply against demand, and bounded rationality is implicit in the process [hence, one key reason for the divergence from classic rational expectations, even if wage or price stickiness is allowed for].

 

There have been many mechanisms suggested by marketing academics to describe how this is achieved in practice; ranging from historical, through cost-plus, to competitive pricing. Even so, it is arguable that the analogue of a 'market price' still enters into the equation in the shape of the expectations of the supplier, and of the purchaser, as to what will be - on the date of future supply - the generally prevailing price which they will be required to meet. As this is a repeat-purchased good, as indeed are most consumer goods, the price can be assumed to be based upon the currently applying price modified by an allowance for the expected inflation over the period in question.

 

This can be simply represented by the equation:

 

            Pf  = Pc(1 + Ie + Iδ)

 

Where Pf = Future Price, Pc = Current Price, Ie = Average Expected Inflation, and Iδ = Individual Deviation from the Average (Expected) Inflation.[this compares, for instance, with the rather more complex form of even the ‘simple’ representation of the rational expectations hypothesis given by Gerrard [23]:

 

                                                t-1 Xet =E(X t|O t-1)]

 

where t-1 Xet is the rational expectation formed in period t-1 of the variable, X, in period t and E(X t|O t-1) is the mathematical expectation of Xt  conditional on the information set O t-1  available in period t-1 (where the whole is characterised by unbiasedness and orthogonality)].

 

The last term allows for the fact that the individual’s information is bounded, and their interpretation of it may not be as rational as many economists’ would wish. If, however, we aggregate a sufficient number of such individual decisions the resulting new aggregate price is:

 

           ΣPf  = ΣPc(1 + Ie + Iδ)

 

As suggested earlier, it may then be reasonably assumed that the individual deviations are effectively random and will sum to zero - indeed that is, by definition, the case for the average price [this is a key feature of the generalised hypothesis, as it is for the rational expectations hypothesis, hence the emphasis on aggregation]. The resulting new ‘market price’ average (Pa) therefore will be:

 

            Pa = ΣPc(1 + Ie)/n   (where the number in the population is n)

or

            Pa = Pc + ΣPcIe/n

 

It is, thus, possible to focus on the overall, average, expectations (of the total population) as to what inflation will be - and this becomes a self-fulfilling (prophetic) expectation.

 

LIMITATIONS OF THE SPECIAL HYPOTHESIS

 

Unfortunately, real life is normally not quite so simple. Even in the case of the Special Hypothesis some individual inputs can distort the overall aggregate. In particular, governments - at the national level - can intervene to influence this process [in contrast with rational expectations theory, which typically only allows for short-run stabilisation policies to succeed]. Indeed, despite economists’ rational expectations, this is arguably the one area where they have learned to intervene in order to manipulate expectations (as the hypothesis allows); most notably, in recent years, by using interest rates as a signal.

 

Beyond this, most issues are significantly more complex - and are linked in complex ways to other issues. In addition, the population's reaction to them is dynamic; changing over time. This dynamic complexity defeats simple analysis; as it has defeated the simple rational expectations hypothesis. In particular, it defeats most attempts at building mathematical models to predict the future; and, in any case, these are typically are based only upon macro factors. Any form of regression analysis, which is typically used to determine the exact relationships in the creation of such models, is defeated on both counts.

 

1 April 2003

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