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The Theory of the Multiplier
European Exchange Depreciation in the Early Twenties
IN A STUDY THAT the author has had the opportunity of making on certain aspects of the economic history of the Continent of Europe in the early nineteen-twenties, he was struck by the similarity in immediate causes and in actual development which characterize the process of exchange depreciation and currency inflation in almost all countries in this area. Of course, as is well known, the extent to which depreciation actually proceeded differed greatly from country to country. Stabilization was achieved in France, Belgium, and Italy at rates of the order of one-fourth of the prewar parity; the stabilization value for the German reichsmark was only 10-12 of that of the old gold mark. Notwithstanding this extreme difference in magnitude, the underlying mechanism which could serve to describe the course of events in all these countries appears to have been substantially the same. It is intended to give in the present paper a brief outline of the main features of this mechanism. Many competent analyses have indeed been performed of the intriguing phenomenon of exchange depreciation in a particular country. Mention should be made of BrescianiTurroni's excellent analytical description of the German experience' and de Bordes' treatment of the Austrian crown.2 A comparative study of a number of European countries has been made by Aftalion.3 From these, as well as from a number of other case studies,4 the major part if not all of the structural equations-to use Frisch's termin the model developed below have been drawn. But in none of these studies are these essential relations made sufficiently explicit to be used as such; and, moreover, as the elimination of what should be considered the very minimum set of structural equations cannot be performed without writing down the relations concerned in mathematical symbols, a full picture of the essentials of exchange depreciation has, it would seem, never been put forward. Nothing more than the very essentials can be given here. It would seem that these alone are already of considerable assistance in clarify
Estimates of Average Service Life and Life Expectancies and the Standard Deviation of Such Estimates
A Fundamental Multiplier Identity
A Regression
The Investment-Factor Method: A Correction
On the Statistical Treatment of Linear Stochastic Difference Equations
Pitfalls in the Statistical Determination of the Investment Schedule
The Role of Money in Equilibrium Capital Theory
WITH THE STUDY OF problems of capitalization, credit, and discount, the peaceful parade of equationally determinate barter economy' comes to an abrupt halt. The systems of equations expressing the conditions of equilibrium theory differ in number from the unknowns to be determined. Equational determinacy is established only by the introduction of money into the system. This conclusion is, I believe, novel in general-equilibrium theory. It is an obvious confirmation to an essentially monetary theory of interest-as distinguished from a real capital theory admitting of short-run monetary dislocations. In its support, demonstration of the following subordinate propositions will be attempted: In a static, but not stationary,2 barter economy it is necessary, first, to posit a plurality of interest rates in order to secure the equality of demand and supply of loans for each of the various goods and services lent in natura.3 It is necessary, second, to provide for yet another plurality of discount rates, to take account of the loan aspect of payments for services made at times other than those at which their final products are sold. It is necessary, third, to establish various fixed relationships, which I call capitalization rates, between the prices of services and the prices of the goods which are their sources, so that individuals may be able to choose rationally between the purchase (sale) of the goods and the purchase (sale) of the services. Under barter, there are no clear interrelationships between these various rates. The lack of interrelationships renders indeterminate each of the three