§ 8 (to Chapter XII, § 4) Interpolating Values of V for 1897-1908

To interpolate values for V we split the difference between two extreme hypotheses: the one of extreme steadiness; the other of extreme variability.

The first of these hypotheses is that V changes in a steady progression from its value of 18.6 in 1896 to its value of 21.5 in 1909. This would imply a perfectly steady growth with time, with no temporary fluctuations. But it seems unlikely that the velocity of circulation of money should not fluctuate somewhat from year to year. We have seen that, theoretically, there is a tendency under normal conditions for money expenditures (MV) to keep pace with check expenditures (M'V'). If this correspondence were perfect, we should have the ratio of MV to M'V', if not constant, at least changing in a perfectly even manner with time. Now this ratio for 1896 is 16.7 per cent and in 1909, 9.6 per cent. If we were to assume a perfectly steady change in this ratio during the intervening 13 years, the resulting value for V would have to vary considerably. This assumption is our second hypothesis of extreme variability. The following table shows the results of the two extreme hypotheses. It will be seen that in general there is no great difference between them.

A supplementary calculation reveals the interesting fact that the "hypothesis of extreme variability" would make money velocity fluctuate approximately with deposit velocity. Splitting the difference between the two extreme hypotheses,—that of extreme steadiness and that of extreme variability,—we have what would seem to be an approximately correct estimate of actual velocity. It is probably correct in most cases for the first two digits. We cannot assume even for 1896 and 1909 that the third digit, that beyond the decimal, is correct, much less can we assume this to be true for the intervening years. But it is sometimes advisable to carry out the calculations to one digit beyond "the last significant figure."