'Floors' and/or 'ceilings' and the persistence of business cycles

In chapters 3,6,7 and 12 of this book and in a number of other recent contributions (e.g. Gallegati et al 2003) the dynamics of Hicks' (1950) discretetime multiplier-accelerator model has been analysed in depth and the role played by 'floors' and/or 'ceilings' clarified. In this chapter we intend to tackle the same problem with reference to models formulated in continuostime, in particular Goodwin's (1951) model of the interaction between the dynamic multiplier and the nonlinear accelerator. Of course, the choice of this model is not casual; rather, it is dictated by a number of factors. First, although Goodwin's article was published in January 1951, in the first issue of volume 19 of Econometrica, it was certainly already in 'incubation' and its main idea 'in the air' some years earlier. This is testified to by the fact tha t the paper (with the provisional title "The business cycle as a self-sustaining oscillation") had already been presented by Goodwin at the American Winter Meeting of the Econometric Society held in Cleveland, Ohio on 27-30 December 1948 (for a summary, see Goodwin 1949). Moreover, from what we read in a footnote contained in the second page of the published version of the paper, we can infer that Goodwin became aware of Hicks' contribution only at the end of his research on the topic, when he was making the final revision of his paper. In short, we can consider it as contemporaneous, if not antecedent, to Hicks' contribution. The second reason for our choice is that, at the same time as Duesenberry (1950), Goodwin (1950) also promptly wrote an important and well known review of Hicks' book. In it, as in Duesenberry's review, it is clearly stated and explained that "either the 'ceiling' or the 'floor' will suffice" (Goodwin 1950, p. 319) in order to maintain and perpetuate the cycle. The final reason for our choice is the fact that in the lit erature (e.g., Le Corbeiller 1958, 1960, de Figueiredo 1958, Sasakura 1996, Velupillai 1990, 1991, 1998, 2004), when reference is made to the 'Goodwin oscillator' (or 'oscillator with a Goodwin characteristic' or 'two-stroke oscillator' or 'one-sided oscillator' or 'two-straight-line oscillator') what is meant is the discovery by Goodwin of an oscillator capable of generating persistent fluctuations with only one barrier. The analysis that follows is an attempt to clarify some of the issues raised in this literature. In order to prepare the ground for this, the next section is devoted to a concise presentation of the model. © Springer-Verlag BerHn Heidelberg 2006.