TIME, SYMPATHY, AND OPPOSITION
Other than the introductory remarks in Chapter I, the effect of time on the equation of exchange has not been mentioned. Economists generally accept a relationship between money supply and prices. The problem is that the relationship relates today's prices with the money supply of two to three years ago.
Although specifics of how the correlation was done were not included, Money and Banking, by David R. Kamerschen (South-Western Publishing Company, 1980) reported that the long term correlation of M2 with CPI, 1920-1976 is .94. A very good correlation indeed. (There are some things that must be taken on faith. The derivation of correlation coefficients is a bit much for this discussion. Let it be sufficient to say that perfect correlation gives a coefficient of 1 and .94 is very close to 1.)
From this correlation it seems inflation could be controlled simply by adjusting the supply of money to keep prices two or three years from now the same as today. Unfortunately it is not sufficient to know the money supply and the desired price level. It is also necessary to know the quantity of goods and services exchanged. But Q, the quantity of goods and services, will not be known for two or three years. It is this difficulty that led Milton Friedman to propose that the money supply be increased at a steady rate equal to the long term growth rate of the economy.
With this growth rate of the money supply the price level can be expected to vary only to the extent the actual growth of the economy differs from the expected growth rate. A very logical argument. However, if all this book were to do were to confirm Professor Friedman's proposal, there would be little point to writing this treatise. So, as already explained in Chapter I, this book will show that;
(1) There is no time lag between changes in the money
supply and changes in the price level;
(2) That the level of prices is also dependent on the
use of money substitutes; and,
(3) That real economic activity is independent of
money supply.
To do all this the correlations presented here will use
measures of money
supply and other data for the same month that the price index is
measured. Because these items change during the month the values
of the prior month will also be used when computing the price
level. That is, the June 1983 value of the CPI will be compared
to the results of the equation of exchange using data measured
for May and the change in that data during June 1983. Likewise
for each of the other months included in this study.
At the beginning of Chapter III the term "sympathy" was used to describe the proportional relationship of items not included in the data. This relationship is accounted for by multiplying each of the data items by a constant. A constant does not account for non-proportional changes in these unmeasured transactions. But, like errors from not knowing the intent of individual owners of cash, checkable deposits, and savings accounts, these errors can be tolerated if the chosen data establishes the relationship with a good correlation.
Returning to the equation of exchange:
It appears that it may be necessary to first determine for each data item whether it represents money exchanges, transactions not in GNP, or exchanges without money. That is, if a data item represents either money exchanges or exchanges without money it would be added to the total. But, if the data item represents transactions not in GNP, then it would be subtracted from the total. And, if the data represents either a positive or negative term but is sympathetic to an item that is of opposite sign then the sign must reflect the greater influence. This is opposition in the data. It is also why it does not matter whether or not we classify each data item as money exchanges, transactions not in GNP or exchanges without money. The correlation process will determine the appropriate classification, not the semantics of an arbitrary definition.P = (MV - T~GNP + E~M) / Q.
We have now addressed all of the elements of the equation of exchange except the one that makes the economist's version a mere tautology. As described in Chapter II, money velocity is the rate that items of money change hands. It is quite probable that money velocity varies with time much like all the other data selected for the correlation. But, unfortunately, I have not found a measure of this value. However, the lack of a measure of money velocity does not prevent use of the equation.
If a constant is used in place of velocity there will be an error introduced that will reduce the correlation of the computed price level in a manner similar to the errors discussed earlier. If velocity changes over time are small and random the error will be small. If velocity changes are large or regular the error will be large. As we shall see, the correlation is very close. Therefore this error and those from all the unmeasured items must also be small. In any case, inclusion of more appropriate data can only improve the correlation. If additional data lessens the correlation, obviously it should be removed as inappropriate.
One more potential source of error is the seasonal adjustments in the data made by the St. Louis Federal Reserve Bank. These adjustments may be appropriate for other uses of this data. For this study the un-adjusted data would be a better choice.