Fisher, Macaulay et Allais face au "Paradoxe de Gibson"

According to the quantitative theory of money, an expansion of the money supply leads both to a decrease of interest rates and an increase of the general level of good prices. This negative correlation expected between these two variables being contradicted by the positive correlation observed – pointed out by Gibson and confirmed by further studies - Keynes refers to the so-called “Gibson’s paradox”. I. Fisher proposed an explanation of this “paradox” with the slowness of the adjustments of interest rates to the rate of change in the general price level. However, F.R. Macaulay showed that, since the delays found by Fisher go up far in the past, this implies a necessary correlation between the price level and the weighted average of past rates of change in the price level found by Fisher. This arises the following question: does the correlation between interest rates and the price level result from a fisherian behaviour of agents or, on the contrary, do Fisher’s results are spurious since due to the correlation between price level and interest rates ? However, Macaulay’s criticism loses its relevance when the delays are short, as observed during periods of hyperinflation and after the Second World War. With respect to this debate, the merit of the Allais’ Hereditary and Relativist (HR) theory is to suggest a synthesis with his “psychological rate of interest” hypothesis. Depending on past values of the rate of change in price level and production, this latter, which equals the “rate of forgetfulness”, represents the general trend of market interest rates. When the memory is long (i.e. the “rate of forgetfulness” is weak), the psychological rate of interest is necessarily correlated with the price level and then explains the positive correlation – which may be more or less stable due to the production effects – between market interest rates and the price level. But when the memory is short (i.e. the rate of forgetfulness high), the HR theory implies both the disappearance of the correlation between interest rate and the price level and the existence of a positive correlation between interest rate and the rate of change in the price level.