RELATION TO MONEY AND PRICES

of r establishes definitely that, characteristically, move-ments in i lag behind corresponding movements in P'.The small numerical value of r suggests that the relationcan be revealed only faintly by P' and i directly. But alittle consideration suggests that the influence of P' or imay be assumed to be distributed in time —as, in fact,must evidently be true of any influence. This hypothesisproved quite fruitful in my studies several years ago,in the course of which the theory of distributed influenceor, if we wish to avoid the implication of cause and effect,of distributed lag was developed in considerable detail. 11

The reader may consult the references cited for details.It must suffice here to point out only the essence of thetransformation of P' into the derived quantity P', meas-uring the distributed influence of sundry P'. Arithmeti-cally, P' is merely a certain weighted average of sundrysuccessive P"s. (See (a) and (b) referred to in the foot-note.) In any specific problem the number of succes-sive P"s that enter into the average P"s depends on thelength of the time interval during which the influence ofany P' is assumed to be perceptible. The weights usedvary in a certain functional form, generally that of askew probability curve. Thus, in applying the theory atleast two parameters are involved: (1) the length of theinfluence interval (which determines the number of P"s

“The theory of distributed influence and lag was developed inci-dentally in the course of my studies of price-trade relations reported inseveral papers. See (a) The Business Cycle Largely a “Dance of theDollar Journal of the American Statistical Association, December,1923, p. 5, top paragraph; (b) Fluctuations in Prive-Levels in TheProblem of Business Forecasting by Warren M. Persons, WilliamT. Foster, Albert Hettinger. Boston , Houghton Mifflin Company, 1924,pp. 50-52; and particularly, (c) Our Unstable Dollar and the So-CalledBusiness Cycle, Journal of the American Statistical Association, June,1925, pp. 179-202.

[ 419 ]