Total factor productivity

Based on Wikipedia: Total factor productivity

The Mystery Number That Explains Why Some Countries Are Rich

Here's an economic puzzle that should keep you up at night: give two countries the same number of workers, the same amount of machinery, and the same raw materials. One produces vastly more than the other. Why?

Economists call the answer Total Factor Productivity, or TFP. It's the ghost in the economic machine—the unexplained portion of output that remains after you've accounted for all the obvious inputs. And according to some estimates, it explains about sixty percent of the differences in economic growth between countries.

That's a staggering number. It means that most of what separates rich nations from poor ones isn't capital or labor at all. It's something else entirely.

Measuring the Unmeasurable

The concept works like this. Imagine you're running a factory. You know how many workers you have, how many hours they work, and what machinery they're using. Economic theory tells you that if you double your workers and double your machinery, you should roughly double your output. But what happens when your output more than doubles? Or when it barely changes at all?

That gap—the difference between what you'd expect and what actually happens—is productivity. Specifically, it's the productivity of all your factors of production combined, hence the name.

The standard way to calculate this uses something called the Cobb-Douglas production function, named after mathematician Charles Cobb and economist Paul Douglas, who developed it in the 1920s. The equation is elegant: total output equals productivity multiplied by capital raised to one power and labor raised to another. Typically, economists weight labor at about seventy percent and capital at thirty percent, reflecting labor's larger contribution to most economic output.

But here's the trick. You can't directly measure productivity. You have to back into it. You measure output, you measure inputs, you do the math, and whatever's left over—the residual—that's your total factor productivity. Economists sometimes call this the "Solow residual" after Robert Solow, who pioneered this growth accounting approach and won a Nobel Prize for his work on economic growth theory.

What's Actually Inside the Black Box?

If TFP is just a residual—the stuff we can't explain—what is it really measuring? Several things, it turns out, all tangled together.

Technology is the obvious answer. Better machines, better processes, better ways of organizing work. A modern car factory produces more vehicles per worker-hour than a 1950s factory not because the workers are stronger or the building is bigger, but because robots weld the frames and computers optimize the supply chain.

But technology isn't the whole story. There's also efficiency—how well you're using the technology you have. Two factories with identical equipment can have wildly different outputs depending on how they're managed, how well their supply chains function, and whether their workers are trained to use the machines properly.

Then there's what economists call "positive externalities." When one company develops a new technique, other companies often learn from it. Knowledge spills over. This is why technology has what economists call "non-rivalry"—your use of an idea doesn't prevent my use of the same idea. My factory's discovery of a better welding process can eventually improve your factory too, even if we're competitors.

The Energy Connection

In recent decades, researchers have uncovered a fascinating correlation: total factor productivity tracks closely with energy use and, more specifically, with how efficiently economies convert raw energy into useful work.

This makes intuitive sense when you think about it. The Industrial Revolution wasn't really about factories—it was about harnessing steam power to do work that human and animal muscles couldn't. The economic transformations of the twentieth century rode on waves of electrification and petroleum. Economic progress, in this view, is fundamentally about getting better at converting energy into stuff we want.

Economists Robert Ayres and Benjamin Warr have argued that when you properly account for energy efficiency in production models, the mysterious TFP residual largely disappears. What looks like inexplicable productivity growth is actually measurable improvements in our ability to convert fuel into motion, heat into manufacturing, electricity into computation.

German physicist Reiner Kümmel reached similar conclusions through different methods, finding that energy input explains much of what Solow attributed to technical progress. The implication is provocative: what we call "technological advancement" might largely be the story of doing more with each joule of energy.

The Human Capital Problem

Early studies of TFP had a measurement problem. They counted workers, but they didn't distinguish between workers with different skills, education, or training. A factory employing a hundred engineers would be measured the same as one employing a hundred untrained laborers, as long as the hours worked matched.

Researchers tried to fix this by using years of schooling as a proxy for labor quality. More education should mean more productive workers, right? But this approach has its own problems. A year of schooling in one country isn't equivalent to a year in another. Quality varies enormously. A 2005 study that tried to correct for these differences found that TFP's contribution to growth was substantially lower than previously thought—much of what looked like mysterious productivity was actually just better-educated workers.

This raises uncomfortable questions about those estimates attributing sixty percent of growth to TFP. How much of that is real technological progress, and how much is just measurement error in how we count labor and capital?

What's Missing from "Total"?

Despite the word "total" in its name, total factor productivity doesn't actually include all inputs. Official statisticians have increasingly preferred the term "multifactor productivity" instead, which at least acknowledges this limitation.

Energy is the most glaring omission, as we've discussed. But there's more.

Public infrastructure—roads, bridges, ports, the electrical grid—enables private production but isn't captured in measures of private inputs. A trucking company's productivity depends heavily on highway quality, but highways don't show up in the company's capital stock.

Environmental costs are similarly invisible. An economy can boost measured productivity by depleting natural resources or polluting waterways, essentially borrowing from the future. The costs are real, but they appear nowhere in the accounting.

Then there are the subtle qualities of the workforce that schooling years don't capture: tacit knowledge, cultural attitudes toward work, institutional trust that enables cooperation. These matter enormously for economic output, but they resist quantification.

The Cambridge Critique

Some economists have raised more fundamental objections. The Cambridge capital controversy—a debate that raged between economists at Cambridge University in England and the Massachusetts Institute of Technology in Cambridge, Massachusetts, during the 1950s and 1960s—challenged the very notion that you can meaningfully aggregate "capital" into a single number.

Think about it: how do you add up a factory building, a computer, a delivery truck, and a patent? They're fundamentally different things. You can express them all in dollar terms, but that valuation depends on interest rates and expected profits—which themselves depend on productivity. The reasoning threatens to become circular.

Even the units of measurement pose problems. Output might be measured in widgets per year. Labor in worker-hours per year. Capital in some amalgamation of machine-hours. When you solve for TFP in the production function, you get something with bizarre, economically meaningless units—a kind of mathematical balancing term rather than a real economic quantity.

To sidestep these issues, official statistics typically focus on growth rates rather than levels. Instead of saying "productivity is X," they say "productivity grew by Y percent." This is more defensible mathematically, even if it still doesn't quite resolve the underlying conceptual problems.

Why It Matters Anyway

Despite all these critiques, total factor productivity remains central to how economists think about growth, development, and the wealth of nations.

The reason is simple: when you decompose economic growth into its components, something has to explain why output grows faster than inputs. Call it TFP, call it multifactor productivity, call it the Solow residual—whatever you name it, the phenomenon is real. Countries do get more productive in ways that can't be explained just by adding more workers or more machines.

And understanding that phenomenon matters enormously for policy. If growth mainly comes from accumulating capital, then countries should focus on investment. If it comes from education, they should focus on schools. But if it comes from that mysterious residual—from technology and efficiency and the organization of production—then the policy implications are different. You need to think about innovation systems, research funding, knowledge diffusion, competitive markets that reward efficiency.

The related Substack article that prompted this exploration examines construction productivity—or rather, the troubling lack of it. While other industries have seen dramatic productivity improvements over decades, construction seems stuck. The same inputs produce roughly the same outputs year after year. Understanding why requires grappling with all the complexities of total factor productivity: what we can measure, what we can't, and what the gap between them really means.

The Big Picture

Total factor productivity is, in the end, a measure of our ignorance as much as our knowledge. It's the economic equivalent of "something is happening here but we don't know what it is."

That's not an insult. Acknowledging what we don't know is the beginning of learning. And economists have made genuine progress in unpacking the residual—finding the roles of energy efficiency, human capital, institutions, and more.

But the fundamental puzzle remains. Some countries, some industries, some firms consistently produce more from less. Understanding how they do it, and how others can learn to do the same, might be the most important economic question there is. The stakes are nothing less than the difference between prosperity and stagnation, between a world where each generation lives better than the last and one where progress stalls.

The mystery number at the heart of economics still has secrets to reveal.