"It is also worth noting that Samuelson...assesses the relevance of capital reversing mainly in terms of the beehavior of the interest rate consequent upon a change in saving behavior: a decrease in current consumption may entail a new steady-state equilibrium in which the interest rate is higher rather than lower than initially. This was indeed unexpected in conventional theory, but its ramifications are rather more serious than Samuelson lets on. The conventional relation between consumption and the interest rate emerges from the operation of the substitution mechanisms that underlie the downward-sloping factor demand functions of the marginalist theory; it is the latter distribution theory that capital reversing undermines." -- Gary Mongiovi, 2002. "Classics and Moderns: Sraffa's Legacy in Economics", Metroeconomica, V. 53, N. 3: 223-241.
"...one must conclude that at present there is no defensible neoclassical theory (in the sense of explanation) of prices and distribution. The onus is on the neoclassicals to show that this is not so. Unless and until they succeed, it seems reasonable to turn to different, non-neoclassical approaches to value and distribution (and employment and growth)." -- Fabio Petri, 1999. "Professor Hahn on the 'neo-Ricardian' Criticism of Neoclassical Economics", In Value, Distribution and Capital: Essays in Honour of Pierangelo Garegnani, Routledge.
"After the stirring, contentious debate over the theory of capital generated by the discovery of the phenomenon of re-switching in the 1960s, one has surprisingly witnessed, in the economic literature, within the course of only a few years, the sudden, one might even say abrupt, disappearance of all discussions on such themes.
The phases through which this state of affairs has come about are themselves an interesting phenomenon, from the view point of the history of economic science, and deserve careful consideration, even at the cost of a brief digression.
The first reaction to the discovery of re-switching was one of uneasy fastidiousness. The intuitive conjecture prevailed that it should be an odd, weird, bizarre or rare case of no empirical relevance whatsoever. The economists who nevertheless originally had to admit it did so with instinctive reluctance, as it clashed with their inherited way of thinking. They used a variety of terms for it, ranging from 'paradoxical' and 'perverse' to 'exceptional', 'inconvenient' and 'anomalous'; a case that 'intuition suggests is unrealistic', and so on (see the numerous quotations in Pasinetti 1966, p. 515, and also Pasinetti 1978). Charles Ferguson, as reported above, was more explicit and candid. He reasserted his instinctive confidence in the neoclassical production function, but admitted that his trust was 'a statement of faith'.
There followed a second phase in which there was a painstaking search for specifying the conditions that could be sufficient to exclude the re-switching phenomenon (on the subject see, for example, Franklin Fisher 1971, Sato 1974, Burmeister 1980). There was moreover a substantial effort to re-interpret the rate of interest as at least expressing the rate of return for society as a whole, when the economic system was changing the proportions between two equally profitable techniques (Solow 1963 and 1967). However, all these efforts did not lead very far. On the one hand the conditions that would be needed in order to avoid the re-switching of techniques proved to be so extremely restrictive as to leave no reasonable possibility of relying on them. On the other hand, in a critique of Solow's attempt to revive Irving Fisher's concept of the 'rate of return', Pasinetti investigated a general discontinuity property of the conception of spectrum of techniques, showing that the vicinity, even an infinitesimal vicinity, of any two techniques on the scale of variation of the rate of profits does not entail at all any vicinity of such techniques (as marginal productivity theory would require) on the scale of variation of their degree of capital-intensity (capital/output, or capital/labour ratios). Capital-intensity might in fact remain quite far apart for the two techniques involved (Pasinetti, 1969). These discontinuity properties have been analysed in detail by J. Barkley Rosser Jr. (1991, ch. 8: 'Discontinuity and Capital Theory'). Thus, new analytical investigation could bring no help for the traditional views; quite the contrary.
Yet there finally came a third very curious phase, which should appear rather strange, given its weak theoretical and empirical underpinning, but which was greeted with relief by the theorists of mainstream economics. The essence of this third phase can be summed up with the following proposition: the criticisms of the traditional theory of capital raised by the phenomenon of re-switching (and consequent reverse capital-deepening) are valid, but only with reference to the neoclassical model conceived in aggregate terms. They do not apply to the neoclassical case of the general economic equilibrium model, conceived in disaggregated terms and based on the behaviour of individuals maximising inter-temporal functions of profits and of utility.
This proposition actually has no objective foundation: phenomena of non-convexity, re-switchings of techniques and badly-behaved production functions, to take an expression that has been widely used ('behaving badly' meaning simply that they behave in a way as not to obey the assumptions of neoclassical economics), are not as has been amply demonstrated a consequence or a characteristic of any particular process of 'aggregation'. They may occur at any time and in any context, aggregated or disaggregated. Various authors have continued to demonstrate this point (e.g. Kurz 1987, Schefold 1997, Garegnani 1998, and others). But so things go. The contrary conviction had taken root and has continued to spread. Above all, the proposition cited above has been trundled out again and again, with no proof, but simply referring back to other sources, which in turn are either insufficient or inconsistent.
The principal one of these sources is represented by an incredibly polemical and dogmatic paper by Frank Hahn (1982), explicitly intended to heap discredit on those economists whom he calls 'the Neo-Ricardians'. With undeniable rhetorical and dialectical skill, Hahn shifted the bases of the whole debate. He admits, without mincing words, that the entire version of neoclassical theory of capital and income distribution, based on aggregate production functions (basically, the whole neoclassical stream of thought descending from Böhm-Bawerk, Wicksell and John Bates Clark) has to be scrapped as inconsistent and incorrect. He then goes on to argue that the correct and relevant version of the neoclassical theory is not that of Böhm-Bawerk, Wicksell and Clark, and not even that of Marshall, but rather the theory that stems from the Walrasian scheme of general economic equilibrium; a scheme which in its modern version is represented by the Arrow-Debreu formulation (Arrow and Debreu 1954, Debreu 1959, Arrow-Hahn, 1971). In this version, the scheme appears as a very general one. Although, in its essential terms, the scheme is a pure exchange model (i.e. a scheme of given resources, which the 'agents' exchange among themselves on the basis of the postulate of maximisation of utility), it can also be reinterpreted in inter-temporal terms, by associating with each resource a quantity index and a time index. In this version, the phenomenon of production becomes a phenomenon of inter-temporal exchange. Thus a framework can be traced out containing a whole range of heterogeneous capital goods. At any given moment of time, the postulates of maximisation (of utility and of profit) by the 'agents' (consumers and entrepreneurs) lead the system to positions of 'temporary equilibrium', generating an overall system of prices for all resources, present and future.
According to Hahn, this framework also includes Sraffa's model as a very special case; namely, as the case where the original heterogeneous goods in the given initial set are exactly in those proportions that generate a uniform rate of profits. But, in general, the 'equilibrium prices' generated by the system will imply rates of interest (and of profit, taken to coincide with the rates of interest) differing from any one (heterogeneous) capital good to another. This does not matter in the Walrasian model à la Arrow-Debreu, given that this model is a price determining model (a point which will be taken up again in the following section). Indeed, the non-uniformity of interest rates is proudly pointed out as a sign of the generality of the model. Hahn admits that the framework might show cases and problems of lack of uniqueness and/or lack of stability of the solutions. However, Hahn claims that the scheme should be immune to the criticisms prompted by the re-switching phenomenon.
But how? The point is precisely here. According to Hahn, in a system with manifold production techniques, equality would still hold between the return on each capital good and the derivative of its production with respect to its input, namely the 'marginal productivities' (in physical terms), although no causal relation could ever be asserted, since all the solutions emerge from a system of simultaneous equations. Hahn admits that there might, of course, be some 'non-convexities' and 'badly-behaved' production functions, in other words that cases of re-switching might occur. So Hahn admits cases of re-switching after all! But here is the ruse: while admitting such cases, Hahn relegates them to the category of difficulties concerning the zones of 'instability'. Now, zones of instability of the system can always occur, in models with heterogeneous capital goods, even in the case of perfectly convex and well-behaved production functions. Indeed, Hahn himself had demonstrated precisely this in an earlier article of his (Hahn 1966) an article, it is to be it noted, written as a critique of dominant theory. Here is therefore how the confusion has been generated a confusion between two different phenomena, namely: a) instabilities, that can in general arise in all neoclassical models with heterogeneous capital goods, and b) the particular phenomenon of re-switching, which by being re-classified as generating instability (a characteristic which is not incorrect, since, among other things, re-switching also generates instability in the capital goods market) is restrictively associated (and confused) with the case previously considered by Hahn.
The paradoxical outcome has been that, instead of taking up Hahn's first finding (1966), which is critical and negative with reference to all the multi-sector models of neoclassical theory, mainstream literature has used Hahn's second article (1982) to assert that the difficulties connected with instability were already well-known.
Conclusion: re-switching had nothing new to tell us. As if the difficulties, when they are already known could, by this very fact, acquire a justification for being ignored, no matter whether they crop up in a different context, where they are reiterated and extended! Surprisingly enough, however, this is precisely what has happened.
Hahn has certainly been very careful not to stress his previous findings strictly logical and negative. Instead, he has adopted the familiar expedient of saying that, of course, there are difficulties; of course these difficulties call for further research; hopefully further research will settle them in the future.
And here we finally come to the non sequitur of the conclusion: the 'Neo-Ricardians' could safely be ignored.
Mainstream economists could not have asked for better. The effect has been to give re-switching the air of an obsession vexing others, and to induce dominant economic theorists not to talk of it any more. The debate soon flagged; in the major economics journal it has been forgotten.
But something even more interesting and intriguing has happened. After only a few years, even the admissions initially made no longer found any mention. Aggregate production functions have made their untroubled re-appearance in the macroeconomic textbooks, without the slightest hint as to their earlier (recognised) logical inconsistencies. It has taken only a few years for them to reappear in papers published in the major journals of dominant economic theory, which at the same time have begun systematically to reject all articles dealing with re-switching as unpublishable. The same authors, who had for two decades been asserting the need to scrap the aggregate neoclassical production functions are now using them quite normally. The typical economics student entering university from the 1980s onwards has heard nothing of the re-switching difficulties involved in the neoclassical theory of capital and income distribution.
It is as if the debate on the choice of techniques had never taken place. Amnesia on such a vast scale can only be explained by more appropriate terms, such as 'suppression' or 'repression' or 'removal'. This is, perhaps, one of the most interesting examples of that process described by Kuhn (1962), through which dominant 'normal' science suppresses, and thus ignores, the cases of contradiction and anomaly it bears within." -- Luigi L. Pasinetti, "Critique of the Neoclassical Theory of Growth and Distribution", 200?