How Do Capitalist Firms Grow?

I’m currently reading Marc Lavoie’s new book Post-Keynesian Economics: New Foundations. This really is the defining text of Post-Keynesian economics today. Anyone who is really interested in Post-Keynesian economics should try to get their hands on it. It is a bit overpriced right now — so you can probably only realistically get it if you order it to your university library — but hopefully Marc can find a way to get it out for lower cost

The book is over 600 pages long and most of those pages are pretty dense. When I’ve finished it I will be either writing a review on the book or a full paper. I’m leaning toward the latter right now as I think there are a few things that might be worth saying. Anyway, for now I just want to discuss a single component of the theory that can be summarised in one neat equation.

In the third chapter of the book Lavoie discusses the Post-Keynesian theory of the firm. In Post-Keynesian theory firms are primarily interested in growth and expansion. They are only secondarily interested in profit accumulation. However, in the theory profit accumulation is a pre-requisite for growth so this largely amounts to the same thing.

The basic idea runs as such: firms want to expand. In order to expand, they must invest. But in order to invest they must accumulate profits. Now, the reader will probably think to themselves “well, they can borrow money to invest too”. This is true. But in the Post-Keynesian theory it is sometimes assumed that the leverage ratio of firms remains somewhat constant. We will come back to this in a moment. Let us now lay out the most basic form of the Post-Keynesian growth equation for the firm. It runs as such:

How should we read this intuitively? The most interesting component from our perspective is the convention that allows the firm to borrow, p. As we can see, when this term increases in numerical value this leads to a higher denominator. This means that a higher rate of growth, g, will be able to take place for a lower rate of profit, r.

This equation is perfectly fine. I can find nothing wrong with it. Lavoie goes on to give some more advanced versions that include the purchase of financial assets by firms. But I will not get into that here.

Lavoie then, however, introduces a notion that I find particularly problematic. He tries to establish a so-called ‘long-run equilibrium growth path’. He does this by assuming “a constant capital to debt ratio”. This I do not find realistic and, in fact, this speaks to a broader problem with Lavoie’s otherwise seminal book: there is no empirical data supporting any of the theory,

Take a look at the following graph. It is by Theodore Gilliland over at Marketminder and it shows the historical leverage ratio of US firms.

What we see here is what we might call a twofold ‘Minsky dynamic’. First of all, it is clear that the leverage ratio is rising over time (in the ‘long-run’, as it were). Second of all it is clear that the leverage ratio rises during expansions and then falls in the ensuing recessions.

So, it is quite clear that it is highly misleading to assume some sort of ‘long-run equilibrium growth path’. Indeed, such an assumption is a wholly imaginary one. Frankly, I find such thought experiments almost as misleading as those undertaken by marginalists. If it doesn’t fit with the real world, leave it out.

Lavoie borrows his idea from Kalecki. Kalecki also wanted to establish something about long-run growth dynamics. So, he assumed that firms would not want to take on higher leverage ratios. He called this the ‘principle of increasing risk’. Lavoie quotes Kalecki as such:

It would be impossible for a firm to borrow capital above a certain level determined by the amount of its entrepreneurial capital. If, for instance, a firm should attempt to float a bond issue which was too large in terms of its entrepreneurial capital, the issue would not be subscribed to in full. Even if the firm should undertake to issue the bonds at a higher rate of interest than that prevailing, the sale of bonds might not be improved since the higher rate in itself might raise misgivings with regard to the future solvency of the firm… It follows from the above that the expansion of the firm depends on the accumulation of capital out of current profits. This will enable the firm to undertake new investments without encountering the obstacles of the limited capital market or ‘increasing risk’. Not only can savings out of current profits be directly invested in the business, but this increase in the firm’s capital will make it possible to contract new loans. (p137)

There may well be some truth in what Kalecki says. Lavoie notes later on that firms with high levels of internal finance have high investment rates. But this does not justify us trying to think in terms of some long-run equilibrium growth paths. The data provided above shows beyond a shadow of a doubt that leverage ratios are simply customs that evolve through time. They are also cyclical in their nature, rising in booms and falling in recessions.

Anyway, the growth equation as laid out above remains a handy tool provided we recognise it for what it is. Lavoie’s book is also fantastic and I cannot recommend it enough. But it would have been helped if Lavoie had consulted the data more often and published this alongside the theory (Kalecki used to do this all the time, after all). I also remain highly skeptical of long-run modelling and of the usefulness of some of the comparative statics approaches that are deployed later in the book. These are some of the issues I want to address in the review when I eventually get around to writing it.

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