Diane Coyle says the fact that different countries have seen different changes in labour's share of income in recent years - with it falling in the US but not UK - shows that "institutions are playing a big part" in driving factor shares. This is true. But it's only part of the story.

I say so for a simple reason. Imagine aggregate wages were to fall for some reason - technical change, globalization, whatever. Would this raise the profit share?

Not necessarily. If every £1 fall in wages causes workers to cut their spending by £1, profits would also fall. In effect, what capitalists gain from the wage cut, they lose from a drop in revenues. As Michal Kalecki wrote in 1935:

One of the main features of the capitalist system is the fact that what is to the advantage of a single entrepreneur does not necessarily benefit all entrepreneurs as a class. If one entrepreneur reduces wages he is able ceteris paribus to expand production; but once all entrepreneurs do the same thing - the result will be entirely different. (Selected Essays on the Dynamics of the Capitalist Economy, p26)

A fall in wages might therefore cause a drop in economic activity rather than a rise in the profit share. To understand whether this will happen, we need to know what happens to the circular flow of income.

We can express this by re-arranging basic national accounts identities. GDP is equal to consumption, investment, government spending and net exports: Y = C + I + G + NX. It is also equal to the sum of incomes: wages, profits and taxes on production (plus depreciation): Y = W + P + T + D. Rearranging these gives us an identity for profits:

P = (C - W) + (I - D) + (G - T) + NX.

This should be intuitive. Profits will rise (ceteris paribus): if consumption rises relative to wages (say because workers save less); if net investment rises (as Kalecki says, capitalists get what they spend); if the government borrows more; and if there's a big trade surplus (say because import prices fall).

My table applies this framework to the US (based on tables 1.1.5 and 1.10 here*). It shows these four factors as a share of GDP in three years: 2000 (when the profit share was unusually low), 2007 and 2017.

Two big things stand out here. One is that the main counterpart to the rising profit share has been a rise in consumption relative to wages. This hasn't happened because people have borrowed more; the savings ratio has risen slightly since 2000. More likely, I suspect, it is due to higher spending by business owners.

Also, note that net investment is much lower than in 2000. This suggests the US is in what Marglin and Bhaduri called (pdf) a stagnationist regime, in which a higher profit share is associated with lower investment.

You could interpret these two developments as signalling that profits are being sustained by short-termism - consumption rather than by investment.

Now, I know that identities don't tell us anything about causality. These numbers are entirely consistent with Diane's point that institutions matter. These can and do put downward pressure on wages. What happens to factor shares, however, also depends upon the behavioural responses to that incipient drop. National accounts identities help identify these responses.

This way of thinking helps explain the IMF's point, that there's a massive heterogeneity in developments in factor shares.

Consider, for example, two possible extremes. In one, an incipient fall in wages boosts capitalists' confidence and hence investment. The upshot could be a boom in economic activity in which the profit share rises but in which the absolute level of wages and employment also rise: this is Marglin and Bhaduri's exhilarationist regime.

At the other extreme, though, capitalists might respond by cutting investment whilst at the same time consumption stays weak - say because workers, fearing further cuts in wages, save more. In this case, we'll get lower economic activity and even a fall in the profit share.

Both responses are possible, depending upon local and temporary factors such as credit constraints and animal spirits.

In this sense - and this is the virtue of Marglin and Bhaduri's paper - general theories about factor shares are insufficient. Instead, as Edmund Burke said: "circumstances are what render every civil and political scheme beneficial or noxious to mankind."

* I've lumped in the statistical discrepancy with capital consumption. Profits are actually the "net operating surplus" which includes rents and self-employment income; this is much higher than corporate profits alone.