This week Thomas Philippon posted a paper (PDF) claiming that TFP growth is linear, not exponential. What does this mean, and what can we conclude from this?

A few people asked for my opinion. I’m not an economist, and I’m only modestly familiar with the growth theory literature, but here are some thoughts.

Background for non-economists

Briefly: what is TFP (total factor productivity)? It’s basically a technology multiplier on economic growth that makes capital and labor more productive. It isn’t measured directly, but calculated as a residual by taking capital and labor increases out of GDP growth. What remains is TFP.

In neoclassical growth theory, TFP matters because it enables economic growth. Without increases in TFP, growth would plateau at some per-capita income level limited by technology. We can increase per-capita output if and only if we continue to improve the productivity multiplier from technology.

What does the paper say?

Philippon’s core claim is that a linear model of TFP growth fits the data better than an exponential model. Over long enough time periods, this is actually a piecewise linear model, with breaks.

To demonstrate this, the two models are subjected to various statistical tests on multiple data sets, mostly 20th-century, from the US and about two dozen other countries. In a later section, the models are tested on European data from 1600–1914. The linear model outperforms on pretty much every test.

*Model D is linear; Model G is exponential*

One theoretical implication of linear TFP growth is that GDP per capita can continue to grow without bound, but that growth will slow over time. Depending on the assumptions you make, growth will converge either to zero or to some positive constant rate.

What to think?

First, I think the evidence Philippon presents at least for the 20th century is compelling. It really does seem that TFP is growing linearly, at least in the last several decades. This is a mathematical model of the Great Stagnation.

Over longer periods of time, however, a pure linear model doesn’t work. TFP, and GDP, clearly grow faster than linear over long periods:

In fact, our best estimates of very long-run GDP growth grow faster than exponential:

(Note that both of these charts are on a log scale.)

Philippon deals with this by making the model piecewise linear. At certain points, the slope of the line discr...

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