The Aggregate Production Function and the Measurement of Technical Change: ‘Not Even Wrong’ by Jesus Felipe and John S.L. McCombie. It is a long technical book. Here is my attempt to summarize one of the main arguments.

Suppose I give you two observations, which might come from otherwise-similar economies or from the same economy at two different points in time:

1. Output per worker = 400, capital per worker = 100.

2. Output per worker = 410, capital per worker = 110.

Can you calculate the elasticity of output with respect to capital?

The answer is “yes” if we are measuring physical units. Bushels per worker. Tractors per worker.

But suppose that we are using national income accounting data. Then our measure of output is GDP. And our measure of capital is income not going to labor. Now, in addition to having well-known aggregation problems in computing output and a capital index, we have to assume implicitly that the marginal product of the 10 additional units of capital is the same as the average product of the first 100 units of capital. But that amounts to assuming that you knew the answer before you even had the second observation. You are only pretending to learn from the data.

This calls into question a whole lot of empirical research purporting to describe economic growth or cross-country productivity differentials.