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Kaldorian and Sraffian supermultipliers: a clarification

This is a post for those interested in demand-led theories of growth. Not long ago I wrote a post on misconceptions about Sraffian economics. Marc Lavoie sent me a nice email about it, and a recent paper he published in Metroeconomica (subscription required), which comments on a paper I wrote with Esteban Pérez (working paper available here). In his discussion of supermultiplier models, which put the multiplier and the accelerator together to explain -- not fluctuations of the level of output around its normal position -- but the determination of trend or normal output. Lavoie says:
"Other post-Keynesians, also assume that non-capacity creating autonomous expenditures are the driving force, rather than investment. Serrano himself refers to Kaldor (1983, p. 9) to provide support for this reversal of causality. Fazzari et al. (2013) assume that there is some unidentified demand component that grows autonomously, in order to tame Harrodian instability; Godley and Lavoie (2007, ch. 11) and, as already pointed out Allain (2015), rely on autonomous government expenditures. Indeed, there is a large Kaldorian literature that relies on exogenous growth components other than business investment, most particularly the whole literature on Thirlwall 's law with its exogenous exports (McCombie and Thirlwall, 1994), as well as Godley and Cripps (1983), with both government expenditure and export sales."
And in a footonte to that passage he says:
"Thus, adding to the confusion over terminology, Pérez-Caldentey and Vernengo (2013) refer to the Kaldorian tradition when discussing models based on induced investment and non-capacity creating exogenous growth components such as Serrano's Sraffian supermultiplier analysis."
So let me clarify our use of Kaldorian, and also why I believe that it is a mistake to refer to the Sraffian supermultiplier as neo-Kaleckian, even though it does have evidently Kaleckian elements. As I understand the distinction that came to dominate demand-led models of growth, there are basically two* main traditions, one that is referred to as neo-Kaleckian, and one that is referred to as Kaldorian.

The first tradition developed from Bob Rowthorn's expansion of Joan Robinson's 1960s model. And because Joan Robinson was influenced by Kalecki, and  Rowthorn, a Marxist author, was seen as Kaleckian, the name stuck. The original model, one must note was wage-led. And causality basically determined whether the authors was Keynesian or Marxist, with Ed Nell famously referring to one author that suggested that causality went from income distribution to growth as Jean Baptiste Marglin. At any rate, Marxist and Keynesian closures, to use the term popularized in this context by Lance Taylor, were special cases of the neo-Kaleckian model. Later developments introduced changes in the independent investment function which allowed for a profit-led closure.

As I noted before, the term Kaleckian is a bit of a misnomer. The current version of the model allows for a profit-led closure, which is not clearly in Kalecki, and, besides its derived from Joan Robinson's model. The Kaleckian feature is that often it is assumed that workers do not save, and capitalists do not consume, for simplification, a classical political economy type of assumption really.**

The genesis of supermultiplier models is more convoluted. On the one hand, the combination of multiplier and accelerator was used to discuss economic cycles, not growth, including by Hicks, who first discussed the idea of the supermultiplier. By the late 1960s, Kaldor moved away from the differential savings or neo-Keynesian growth models (sometimes referred to as Kaldor-Pasinetti or Cambridge growth model), and adopted the supermultiplier model, formalized by Thirlwall in the 1970s. The model assumed as a simplification that exports were the only autonomous component of demand. In accordance with the accelerator, investment was seen as derived demand. That is the main difference with the so-called Neo-Kaleckian models, namely: there is no independent investment function.***

The idea of the supermultiplier was later, in the 1980s and 1990s, developed by Bortis and Serrano,**** both authors sharing a Sraffian perspective. In these versions, autonomous spending was not restricted to exports, and government spending was also relevant. The term Sraffian or classical-Keynesian has been used to describe these models. In essence, they are Kaldorian models, since investment is derived demand, as much as in Thirlwall's model. In this sense, even though the Kaldorian models a la Thirlwall are a special case of the Sraffian supermultiplier, as discussed here in my debate with Jaime Ros (in Spanish), and by definition more general than the export-led growth model, they came later, and can be seen as a development within this tradition.

So certainly the intention is not to create confusion. In my view, models with an independent investment function are broadly speaking neo-Kaleckian, while models in which investment is derived demand are Kaldorian. And there are differences between models within those broadly defined traditions.

* All taxonomies are somewhat arbitrary and one might see some sub-divisions from the two main branches discussed here as standing in the same footing, for example, some might argue for an explicitly Marxist tradition.

** Goodwin predator-prey models, which have become quite fashionable, can be seen as a variation of these neo-Kaleckian models.

*** I think these Cambridge models have been completely abandoned since the 1960s, and that is the reason why I don't have three types of models in my taxonomy. They are a historical curiosity, associated to a response to the Harrod instability problem, at a time when full employment seemed like a stylized fact in advanced capitalist economies. For a clear explanation of the implications of the different model closures see the paper by Franklin Serrano and Fabio Freitas here.

**** The Sraffian versions of the supermultiplier model also assume differential savings by workers and capitalists, as many other classical political economy inspired models, and in that sense have Kaleckain features. But they are not neo-Kaleckian, since there is no independent investment function.

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