On the Shoulders of Wicksell and Cassel

The formation of the Stockholm School was strongly influenced by works of Knut Wicksell and Gustav Cassel, the key figures in the prior generation of Swedish econo­mists. Wicksell’s Interest and Prices (1898 [1936]), with its theory of cumulative changes

in the price level, opened an avenue for thinking about macroeconomic dynamics, while Cassel’s Theory of Social Economy (1918 [1923]) provided the starting point.

Myrdal’s approach met with a fundamental critique from young Lundberg, who was a student of both Cassel and Myrdal at the University of Stockholm. In an article “On the concept of economic equilibrium”, which was based on his licentiate thesis, Lundberg (1930 [1994]: 35) pointed out that expectations of price changes are not independent of the given price structure, “except when changes are wholly exogenous to the economic context”. He argued that Myrdal, moreover, had failed to show how a general equilib­rium would develop from a market constellation with incongruent expectations. If, on the other hand, “individuals’ expectations are ‘rational’, in the sense that they are real­ized”, the analysis would not supersede Cassel’s static theory. “By assuming that the time distance does not have any effect, the time element... is eliminated” (Lundberg 1930 [1994]: 34).

Lundberg’s early use of the notion of “rational expectations” is noteworthy. Yet it was Lindahl who gave it a precise meaning by examining the conditions under which “the individual anticipations of coming price developments are to a certain extent the causes of the actual developments themselves” (1939: 147). In his “Place of capital in the theory of price” (1929a), translated in his Studies in the Theory of Money and Capital (1939: pt III), Lindahl addressed “the problem of price formation” by taking “into account some of the complications due to the existence of a time factor in production, i.e. to the complex of problems where the theory of capital and interest and the general theory of price meet” (1939: 271). The valuation of capital goods was clearly a Wicksellian theme, but Lindahl was critical of the Bohm-Bawerkian approach used by Wicksell. He started, like Myrdal (1927), from the static Walras-Cassel system, but used a different track for its extension to dynamics.

In order to analyse such a dynamic process, we imagine it to be subdivided into periods of time so short that the factors directly affecting prices, and therefore also the prices themselves, can be regarded as unchanged in each period. All such changes are therefore assumed to take place at the transition points between periods. (Lindahl 1939: 158)

The first exposition of Stockholm-style sequence analysis is thus found in Lindahl (1929a), where the examination of the “pricing problem” proceeded step by step from perfect foresight and stationary conditions to imperfect foresight and dynamic condi­tions. In this context, Lindahl (1929a) made essential contributions to the concepts of intertemporal equilibrium and temporary equilibrium, independently of Hayek (1928) and prior to Hicks (1939), even though he did not use these terms at the time (see Kurz and Salvadori 1995: 456-58). Intertemporal equilibrium is characterized by the correct anticipation of all changes at transition points, such that the prices, quantities and interest rates of all periods are simultaneously determined. This construction was just an intermittent step from static to dynamic analysis in “approximation to reality”, so Lindahl (1929a: s. 4) relaxed the assumption of perfect foresight and discussed changes in intertemporal price relations that are connected with unforeseen gains and losses and subsequent shifts of budget constraints. Assuming that the unforeseen changes occur at the transition points between the periods, Lindahl (1929a) described the latter as tempo­rary equilibria.

In his classic essay on “The means of monetary policy”, included as “The rate of inter­est and the price level” in the Studies (1939: pt 2), Lindahl took the temporary- equilibrium method to its limits by applying it to a generalization of Wicksell’s (1898 [1936]) theory of cumulative inflation and deflation.

In The Means of Monetary Policy, Lindahl (1930 [1939]) reversed the procedure. Like Wicksell (1898 [1936]), he chose the setting of a completely centralized pure credit economy, in which the central bank sets the level of interest rates autonomously. Lindahl explored “the cumulative process caused by lowering or raising the level of interest rates” (1939: ch. 2) in different scenarios, varying the assumptions about the states of informa­tion (perfect, imperfect foresight) and expectations (static, adaptive, forward-looking), the degrees of unemployment, capacity utilization and investment irreversibility in dif­ferent sectors, and the structure of interest rates. Each scenario was analysed “as a series of temporary equilibria, between which there occur unforeseen events with consequent gains and losses” (Lindahl 1939: 11). The immediate result of an unexpected lowering of the interest rate is an increase in all capital values, greater for long-term investments and smaller for short-term investments. In the following periods markets would clear, but not always at the expected prices. The size and distribution of gains and losses is determined by the constellation of assumptions that defines the scenarios.

Lindahl (1930 [1939]) was nevertheless critical of policy strategies that attempt to exploit this redistributive income mechanism. He was convinced that people would learn from their inflation experience, such that the state of expectations would turn from static to adaptive and even forward-looking. In the end, inflation might accelerate to the extent that it would become “necessary to arrest the movement before the amount of capital appropriate to the lower rate of interest has been accumulated” (1939: 182-3). In con­trast with much of modern mainstream macroeconomics, Lindahl considered rational expectations to be endogenous, both to inflation and to credible anti-inflation policies. He was also critical of Wicksell’s concept of a “natural or real rate of interest” and dem­onstrated that, outside a one-good economy, “the real rate of interest does not depend only on technical conditions, but also on the price situation, and cannot be regarded as existing independently of the loan rate of interest” (1939: 248).

In an additional note to the 1939 translation of the 1930 essay, Lindahl qualified his views on the cumulative process and the neutral rate of interest. In closer connec­tion with Wicksell’s original approach, he now argued that, compared to his earlier temporary-equilibrium approach, a sequence analysis, “by which economic processes are regarded as series of successive disequilibria, must undoubtedly be held to be more generally applicable” (1939: 260-61, emphasis added). Lindahl also acknowledged that prospective profit rates could systematically differ from the actual loan rates of interest, and that the normal rate of interest (capital market equilibrium) is not necessarily neutral with regard to the expectations of the public, the distribution of income or the volume of production. In all this, Lindahl explicitly reacted to Myrdal’s critique of his 1930 essay.

In the 1931 volume of Ekonomisk Tidskrift (now the Scandinavian Journal of Economics), Myrdal published a long article “On the theoretical concept of monetary equilibrium”, advertised by its subtitle as “a study of the ‘normal rate of interest’ in Wicksell’s monetary theory”. A more widely read German version appeared in 1933 in an anthology edited by Friedrich A. Hayek; it was translated into English and published as a monograph in 1939. Together with Lindahl’s Studies (1939), Myrdal’s Monetary Equilibrium (1939) has come to be regarded as a landmark contribution to the macroeconomics of the Stockholm School. The Swedish version contains a critique of Lindahl (1930 [1939]), through which Myrdal attempted to reconstruct Wicksell’s concepts of monetary equilibrium and cumulative processes by way of immanent criticism. The German and English versions were largely cleared of critical comments on Lindahl and presented as an extension of the dissertation project, intended “to include anticipations in the monetary system” (Myrdal 1939: 32; cf. Hansson 1982: ch. 6).

Myrdal (1931) examined the three conditions by which Wicksell (1898 [1936]) had defined monetary equilibrium: “The ‘normal rate of interest’ must... (1) equal the marginal technical productivity of real capital (i.e. the ‘real’ or ‘natural’ rate of interest); (2) equate the supply of and demand for savings; and, finally, (3) guarantee a stable price level” (Myrdal 1939: 37-8). Myrdal went even further than Lindahl in demonstrating that Wicksell’s conditions were either imprecise (2) or false (1 and 3). He showed that Wicksell’s notion of a natural rate of interest was incompatible with his assumptions of a credit economy and of innovations as causes of the shifts in the “yield of real capital” that generate cumulative inflation. In a non-stationary monetary economy, the yield of real capital includes expectations about money prices and loan rates of interest. Hence, changes in the levels of prices and interest rates feed back to the yield of real capital in terms of prospective profitability. Myrdal (1931 [1939]: 84-97) accordingly redefined the equilibrium rate of interest as the rate at which the “cost of production of new invest­ment” equals “free capital disposal” in terms of “savings proper” and “value change defined as anticipated depreciation minus appreciation” of the investment in question. The equality of the value of real capital and its costs of reproduction implies the equal­ity of investment and saving. In this way, Myrdal’s definition of monetary equilibrium essentially anticipated the formulation of Tobin’s q.

Another innovation of Myrdal’s study helped to make the analysis of cumulative processes more operational by describing them in terms of balanced bookkeeping. This innovation, which was more clearly developed in the German version (1931 [1933]), was the distinction between ex ante and ex post, i.e. between expected and realized values, or between plans and outcomes (1939: 45-7, 116-25). If the ex post values correspond to the ex ante values, the economy is in a state of monetary equilibrium; if they do not, unplanned adjustments of prices, quantities and the capital stock take place, eventually amounting to a cumulative process. Myrdal (1931 [1939]) criticized Lindahl (1930 [1994]) for being unable to analyse such out-of-equilibrium adjustments. Myrdal’s own treat­ment of cumulative processes was largely limited to verbal conjectures about the “inner mechanics of the depressive process”, induced by a tightening of the credit conditions (1931 [1939]: 164-9). Yet his ex ante/ex post terminology stimulated formal exercises in disequilibrium analysis, carried out by Hammarskjold (1933), Lundberg (1937) and Svennilson (1938) in their doctoral dissertations, and by Lindahl in preparation of his Studies (1939). Despite the differences in publication dates, these works were essentially composed and discussed between 1932 and 1935.