The Residual
Start with a question that seems easy. An economy produces more this year than last. Why?
There are three obvious answers. Perhaps more people worked, or the same people worked longer. Perhaps there was more equipment for them to work with — more machines, more buildings, more vehicles, more computers. Or perhaps something else happened. The first two you can count. Hours worked are counted, imperfectly but honestly, by household and payroll surveys. The capital stock is counted, much less honestly, by taking historical investment and depreciating it according to assumptions about how long things last. So you can take the growth in output, subtract the part explained by more hours, subtract the part explained by more capital, and look at what is left over.
What is left over is called total factor productivity, and it is the number that decides whether a country gets rich.
Notice that this is a definition by subtraction. TFP is not measured; it is inferred, as the gap between what happened and what you can account for. Moses Abramovitz, who did some of the earliest work of this kind in the 1950s, described the residual, with a frankness that has never quite been forgiven, as some sort of measure of our ignorance. He meant it precisely. Everything you have failed to measure, everything you have mismeasured, every improvement in how work is organised, every advance in technique, every change in the quality of workers or of machines that your capital and labour series failed to pick up, and every error in your capital and labour series themselves — all of it lands in the residual, because the residual is defined as the bit you could not explain.
This has two consequences that matter for what follows. The first is that when TFP growth is high, it is genuinely ambiguous whether the country has become cleverer or the statisticians have become confused, and there is no internal test to distinguish them. The second is that a technology which arrives largely as more capital will show up first as capital deepening, not as TFP — as workers having better tools rather than as the economy having found a better way to be. Those look identical from the shop floor and completely different in the national accounts.
It is a strange discipline that builds its central concept out of its own failures, and stranger still that it works as well as it does. But it does work, in the specific sense that the residual, over long periods and across many countries, tracks the things we independently believe to be true about technological progress. It rose in the mid-twentieth century. It fell after 1973 in a way nobody has ever satisfactorily explained. It rose again in America between about 1995 and 2004 and then fell back. The residual knows something. It just cannot tell you what.
from Everywhere But the Statistics: The Macroeconomics of Artificial Intelligence, Told Through Its Bottlenecks (2026)
