Capital Theory and Dynamic Methods

Lindahl’s contributions to the development of dynamic methods emanated from the elaboration of his macroeconomic theory in the late 1920s and early 1930s. In his essay “The place of capital in the theory of price” (1929 [1939]) Lindahl was led to the formula­tion of the concept of an “intertemporal equilibrium” from a critique of Wicksell’s treat­ment of capital.

The difficulties here mentioned are associated with the stationary setting of the problem. On account of its artificial and very special assumptions the static problem has little or no con­nection with the phenomena determining prices in the real world. Therefore the attempt must be made to build up on this foundation an improved analysis which will have more general validity. (1929 [1939]: 317)

This he attempted to do by formulating an intertemporal equilibrium model which extends over a finite number of periods (1929 [1939]: 322-8). Lindahl’s model has been praised by Gerard Debreu as a precursor of his own (1959: 35), but exhibits some impor­tant conceptual differences with regard to the Arrow-Debreu model. Lindahl conceived of an intertemporal equilibrium as a depiction of an efficient adjustment path to an unexpected change in the long-period data, which (in the absence of further changes in data) terminates in a stationary state. He noted explicitly that this way of approaching the problem of capital and interest opens up the possibility of treating “all existing capital equipment [in the initial period] as original”, while capital goods which are “produced in the periods included in the analysis...

However, in the last section of the essay (Lindahl 1929 [1939]: 348-50) he substituted imperfect for perfect foresight, and in his next essay, Penningpolitikens Medel (The Aims of Monetary Policy) (1930 [1939]), he abandoned the intertemporal equilibrium method, for the case of imperfect foresight, and replaced it with the notion of a sequence of tem­porary equilibria. This concept was soon afterwards adopted (and slightly reformulated) by John Hicks in Value and Capital (1946: ch. 9, first published in 1939), but Lindahl was not satisfied with it. Because the method of temporary equilibrium could not handle unforeseen events that occur during a period, and thus failed to generate causal sequences, he replaced it with the method of “sequence analysis” in the first part of his Studies (1939: 21-69). Lindahl sought to develop such a causal sequence analysis by incorporating Myrdal’s distinction between ex ante and ex post: he first analysed a single period, in which ex ante plans determine ex post results, and then linked the periods together by means of a continuation analysis, in which the ex post events of the preceding period lead to revised ex ante plans in the subsequent period. Hansson (1982) provides a comprehensive account of the development of dynamic methods in the interwar period by members of the Stockholm school.