Solow residual: Total factor productivity and the U.S. economy

For decades, the productivity of American workers seemed stuck. No matter how hard people worked or how much capital was invested, productivity, except for a few years, never seemed to move much.

That may be changing. Last year, American productivity improved by 2.7%, and gained steam in the second half with a 4% increase, according to the traditional measurement released by the Labor Department.

That is the type of productivity that the U.S. economy has not experienced since the period between 1995 and 2004, when it averaged 3%.

It is most welcome news for economists and policymakers, given the implications regarding growth, employment, inflation and general living standards, all of which weigh on fiscal and monetary policy decisions.

Economists, after all, are not given to doe-eyed optimism. But the productivity story that is emerging—especially from an alternative measurement called total factor productivity—suggests that the economy may indeed be on the verge of a productivity renaissance.

Total factor productivity captures capital investments as well as labor, and is seen by many as a better measure of productivity. A recent study by the San Francisco Federal Reserve found that total factor productivity grew by a robust 4.99% in the fourth quarter of last year after adjusting for factors such as labor, capital, utilization and worked hours.

Absent those adjustments, total factor productivity advanced by 2.62%, the study found. Still, the adjusted 4.99% figure was much higher than the commonly used labor productivity measure released each quarter by the Bureau of Labor Statistics (BLS). Labor productivity growth, calculated as output per hour worked, was at 3.2% in the fourth quarter.

The San Francisco Fed uses total factor productivity, which is widely known as the Solow residual, named for the late Nobel laureate Robert Solow. The Solow residual is best understood as the portion of overall economic output that cannot be adequately explained by the factors of production or the accumulation of capital and labor.

The San Francisco Fed's measure is our preferred metric of productivity, as it strips away the changes in labor and capital input built into the BLS’s labor productivity measure. It provides a better way to identify the impact of technology and changes in economic structure on underlying productivity.

The increase in total factor productivity, especially in back-to-back quarters, is an encouraging sign that the significant investments that businesses have been making might have finally started to spur real changes.

While it remains too early to claim that such changes are permanent, there are reasons to believe the economy is on the cusp of a boom in productivity in the next decade or so, spurred by the adoption of artificial intelligence, increased automation, the shift to remote work models, and industrial policies.

If productivity continues to rise, it could be the economic tide that benefits everyone.

It is important to note that the recent innovations around artificial intelligence and quantum computing are still too early in their life cycles to have caused the recent improvement in productivity.

In addition, some of the improvement in productivity may be a result of the rebound in the economy following the historic shocks caused by the pandemic.

But the pandemic raises another question: How much of the rise in productivity is attributable to people working from home?

Approximately 20% of the American labor force now works from home, according to the BLS. One would anticipate that the recent improvement in total factor productivity would capture the impact of this recent trend.

While we have no definitive evidence that the shift to remote work has influenced total factor productivity, that trend is now going to be part of the economic narrative around the long-term structural changes caused by the pandemic.

The policy implications are simply too important to ignore.

What is special about total factor productivity?

Total factor productivity is a measure of productivity that accounts for the changes in labor and capital. The measure is calculated based on how we model the economy using a production function that includes labor and capital as inputs.

The simple labor productivity measure, or output per hour, does not account for the changes in capital or other factors, an approach that could be misleading.

For example, when a company invests in new equipment, which would increase the total level of spending output, that investment would not necessarily increase how many products its employees could produce, yet the measure of labor productivity would increase.

By controlling the increases in capital and labor, total factor productivity is what is left that cannot be explained by either of those factors—hence the Solow residual. In general, total factor productivity represents an improvement in technology or a shift in economic structures.

The San Francisco Fed takes the metric one step further by introducing a utilization-adjusted version based on research by Susanto Basu, John G. Fernald and Miles S. Kimball in 2006. That version "sought to adjust for a range of non-technological factors that affect measured total factor productivity, of which variations in the utilization margin—i.e., the intensity margin for the workweek of capital and labor effort—are only one."

After examining the Solow residual and its impact on the economy, using any other method to measure productivity seems inadequate.