Evan Soltas
Feb 26, 2012

Black Death, Silver Lining?

Capital deepening might explain the timing of the Renaissance.

Under the Banner of King Death
I'm going to warn you in advance that this is a very weird post.

One of the key contentions of the modern understanding of productivity is that it is determined by the ratio of capital inputs to labor inputs. In many theories -- the Solow growth model, the endogenous growth model -- this is in fact a core assumption that when this ratio shifts towards capital, then productivity increases; when it shifts towards labor, productivity falls. Economists refer to the former as capital deepening and the latter as capital shallowing.

There are two ways to make the ratio change, obviously: you can increase or decrease the supply of labor or capital. I suppose I wonder about the validity and strength of this supposition that capital intensity is the most relevant consideration in productivity. From my own micro and anecdotal perspective, the level of capital seems not to matter as much as the efficiency with which it is employed. I suppose I worry that, in the aggregate, this capital efficiency may be so variable across economies and time series so as to make productivity not a function of capital intensity.

Imagine a two-sector economy, for example, with two different and not-substitutable types of capital. (Perhaps suppose the first good produced is oranges, the second is steel; the two relevant capital goods are mechanical pickers and forges.) When one sector acquires the other's capital, there is no change in productivity; only when the sector gets the matching capital are there productivity gains. Now obviously this example is a little strained -- how many orange farms do you see with forges? Not many.

But I think this model gets us somewhere, because I think the argument that there is perfect efficiency in how capital is employed at all times is silly. In other words, it stands to reason that on the margin, some firms will have misemployed capital. (Indeed, Schumpeter's model of creative destruction relies on this process of the discovery of relative inefficiencies to cause firms to exit the market and thus to raise average productivity.) There will be some orange farms with forges, to use our absurd example -- less absurd is the notion that the steel firm will not have optimally arranged supply chains or assembly lines, or that the orange farm will not have optimally trained workers. But the quantitative effect of misallocation of capital causing lower capital productivity is still there.

Now that we've sufficiently undermined the idea that capital intensity is all that matters, let's ask another question: what evidence to we have of the relationship of capital intensity and productivity in the first place? I couldn't find any reviews of empirical evidence in the scholarly literature -- if anybody knows of one, please send it my way -- but from my own and admittedly quick research, the data suggest a weak effect, at best, of capital intensity, with capital efficiency or other variables seemingly far more determinative of the level and growth of productivity.

In particular, I looked at two instances -- the first ones I could think of -- where I would expect sharp and high-magnitude changes in capital intensity: the Black Death or epidemic of bubonic plague in Europe and the return of American men from World War II. This is a very strange pairing, for sure. But the reason I've chosen these two is because they represent substantial changes in the level of labor available for production -- the first being a decrease of 25 to 60 percent of the labor force, the second being an increase of 25 percent, making some simplifying assumptions. It's hard to find similar changes in the capital stock alone -- when a large amount of capital gets eliminated, as in total war, the changes in labor force tend to be significant as well.

What I found was in neither of the two instances did productivity increase as much as a function of solely capital intensity for productivity would suggest. Wages rose in Europe after the Black Plague, the price of land and other forms of capital fell, according to one study, and I'm tempted to suggest that the Renaissance was the result of capital deepening, but the evidence is frankly weak. Another study found that the trend of agricultural productivity in England did not change as a result of the change in the equilibrium prices of labor and capital. A study of the 1918 influenza epidemic, which reduced the labor force permanently by 1 percent in some states (it probably reduced the labor force temporarily by more), did find some capital deepening effects, however.

Looking at the departure and return of American men during World War II, we find high volatility in productivity growth but no clear shift suggestive of a productivity deepening and then shallowing.

What the evidence more strongly supports is that capital efficiency is what really matters. Although private nonresidential fixed investment grew at roughly the same rate since World War II, trend productivity growth in manufacturing has moved around, with the well known 1970s productivity slowdown and the acceleration in the 1990s. This suggests that what matters is how the capital is being employed, not how much is acquired, has an empirically larger effect on productivity.

So it looks like we can't expect renaissances from capital deepening alone -- capital efficiency gains represent the best way forward.