Briefly stated, what the process entailed is that confronted with the fact that there is no possible way to relate some measure of capital with its remuneration (the idea that abundant capital would lead to a low level of remuneration, i.e. a low rate of interest, and the analogous one that full employment of capital could be obtained with a sufficiently low rate of interest) the mainstream reverted to the Arrow-Debreu (AD) notion that different types of capital had different remunerations and there was no tendency to a uniform rate of profit (interest). That, as noted by Garegnani, was a departure from the traditional method of economics. Up to the 1930s all economists, including the marginalists (neoclassical) ones did follow it.
Note that the long-term, associated with the uniform rate of interest (or profit), is a methodological instrument, not a particular period of chronological time. The long-term is just a period in which no variables are constant or fixed, and the process of competition, that allows for new entrants in every sector (with perfect competition) to lead to a uniform rate of interest. The short-term is by symmetry a situation in which something precludes the long-term situation to be achieved. For example, a typical short-term macroeconomic assumption is to assume a given level of productive capacity. The demand effect of investment (demand for equipment and installations) is taken into account, but not the capacity effect (the increase in the number of machines and plants).
That's why this comment by Miles Kimball (a supply-side liberal, talk about oxymoron) is so revealing of the confusion that now dominates the mainstrem. He says:
"To think clearly about economic fluctations at a somewhat more advanced level, I find I need to use these four different time scales:Yes, that now passes for clarity of thinking. Short-term is a period of chronological time, long-term is conceptual methodological position. The confusion is compounded by the fact that he is trying to clarify what he sees as "a lot of confusion about the natural interest rate ... [and] the main source of confusion is that there is both a medium-run natural interest rate and a short-run natural interest rate." The natural rate is by definition a long-term position.
- The Ultra Short Run: the period of about 9 months during which investment plans adjust—primarily as existing investment projects finish and new projects are started—to gradually bring the economy to short-run equilibrium.
- The Short Run: the period of about 3 years during which prices (and wages) adjust gradually bring the economy to medium-run equilibrium.
- The Medium Run: the period of about 12 years during which the capital stock adjusts gradually to bring the economy to long-run equilibrium.
- The Long Run: what the economy looks like after investment, prices and wages, and capital have all adjusted. In the long run, the economy is still evolving as technology changes and the population grows or shrinks."
Old marginalists, like Wicksell or Marshall didn't think the system was at the natural rate in the short-run. It gravitated around it in the long-term. This idea of a short-run natural rate, derives from the AD short-run notion of a system that is always in equilibrium. And then he does use an aggregative version of an ISLM model (which is a long term sort of equilibrium notion). But he has no clue about the capital debates and its consequences. Oh well.