Here is another excerpt from “Is the rate of scientific progress slowing down?”:
First, many scientific advances work through enabling a greater supply of labor, capital, and land, and those advances will be undervalued by a TFP metric. Let’s say someone invents a useful painkiller, and that makes it easier for many people to show up to work and be productive. Output will rise, yet that advance will show up as an increase in labor supply, rather than as an increase in technology or scientific knowledge. Similarly, a new method for discovering oil may boost output, but that will be classified as an increase in oil supply, even though it does properly represent a form of scientific progress. TFP is best at measuring scientific and technological advances that are superimposed on top of an existing supply of the other factors of production. If, for instance, you imagine a series of capital and labor resources at a factory, and someone develops a new formula for combining those resources more effectively, this will be picked up very effectively by standard TFP measures.
The more general problem is that many scientific and technological advances are embodied in concrete capital goods. Again, the TFP measure does best when the supply and nature of capital is fixed, and a new idea makes that capital (and associated labor) more effective. But what happens when the new idea is itself embodied in a concrete capital good? If a hospital equips its surgeons with iPads, or with Augmented Reality glasses, to make them more effective in the operating room, as a first order effect that measures as an increase of capital expenditures by the hospitals rather than as an innovation. Health and later output will increase, but will we really know if it is due to better ideas or just more investment? It will appear to measure as new investment. Capital expenditures and TFP are not so easily separated, whether at the conceptual or the practical measurement level.
Similarly, separating TFP from labor expenditure is not always so simple either. If a worker generates and carries forward a new scientific idea for producing more with a given amount of labor, that measures the same way as the worker being taught greater conscientiousness and producing more. Yet the former is (ideally) TFP and the latter is not, but both will count as an increase in the quality of labor input in the same way.